EAST RUTHERFORD, N.J — The Chiefs had every reason to believe they would roll on Sunday against the New York Giants.

For one, they were facing a 1-8 team, one whose effort in a loss to previously winless San Francisco a week ago was questioned by many.

Secondly, the Chiefs were coming off the bye week, which has historically meant a likely victory for coach Andy Reid, who entering Sunday was 16-2 — and had never lost to a sub-.500 team — after bye weeks.

But there’s a reason the phrase “any given Sunday” exists in professional football. In today’s NFL, anybody can beat anybody, given the right circumstances.

And Sunday’s result for the Chiefs — a 12-9 overtime loss to the hapless Giants before an announced crowd of 76,363 at MetLife Stadium — was an example of that.

“It’s tough to win in the National Football League — there’s parity,” said Chiefs coach Andy Reid, whose team fell to 6-4. “It doesn’t matter if you are 1-8 or whatever it might be.”

That explains why the Giants came out and played hard — and well — despite being mired in a disaster of a season. Not that the Chiefs were surprised.

“I saw this effort, and this attention to detail, coming from a mile away, just because of all the stuff you heard in the media about their coaches challenging them,” Chiefs tight end Travis Kelce said. “Our job is to go out there and match it and play ball and we fell short.”

Unlike the Chiefs’ 28-17 loss to Dallas before their bye week, Reid was pleased with the energy his team played with. His problem was with the execution.

“I thought we had a good week of practice ... I thought the guys had good energy,” Reid said. “We just weren’t able, with the turnovers, to take care of business offensively.”

Indeed. Because while the defense could have been better — the Chiefs only hit Giants quarterback Eli Manning once and they eventually surrendered the game-winning scoring drive — they still gave up just 12 points, so they theoretically did enough to win.

That said, the blame for this one lies mainly at the feet of the Chiefs’ suddenly befuddled offense.

With the Giants focused on taking away the run on a day with 23 mph winds — rookie running back Kareem Hunt managed 73 yards on 18 attempts despite the extra attention — the passing offense failed to punish the Giants consistently. Three interceptions and a complete inability to capitalize in the red zone (0 for 3) against the league’s 31st-ranked defense resulted in Kansas City’s fourth loss in five games following a 5-0 start.

The Chiefs’ issues started early Sunday, with a series of miscues leading to New York’s first score of the game.

On their second drive of the game, the Chiefs — who have apparently run the tight end-shovel pass a few too many times — gave the ball right back to New York. Giants defensive tackle Damon “Snacks” Harrison sniffed out the shovel pass, drilled tight end Travis Kelce upon impact and snatched it away for an interception, giving New York’s offense the ball at the Chiefs’ 26.

Considering the Giants’ offensive ineptitude — they entered the game ranked 25th in total offense — there was no guarantee they’d kick a field goal, let alone score a touchdown, despite the superb field position.

Fortunately for them, however, the Chiefs’ defense was in a charitable mood. Manning, 36, isn’t much of a scrambler, but he promptly ran for a first down on third-and-8. Then, on third-and-7, Chiefs cornerback Marcus Peters was whistled for pass interference, giving the Giants the ball at the 1. They scored one play later when running back Orleans Darkwa (20 carries, 74 yards) dove across the goal line.

The Giants missed the ensuing extra point, and the Chiefs went to work putting together a drive that even included a first-down conversion on second-and-19, courtesy of a 21-yard completion from quarterback Alex Smith (who finished 27 of 40 for 230 yards and two interceptions) to Kelce (eight catches, 109 yards).

But the drive ultimately stalled and ended with a 31-yard field goal by kicker Harrison Butker that made it 6-3 with four minutes left in the half.

The bad football continued in the second half, as both units sparked at times but never put it all together. The Chiefs advanced all the way to the Giants’ 36 before petering out, while the Giants advanced to the Chiefs’ 33 before a fourth-and-9 throw to tight end Evan Engram fell incomplete.

The Chiefs’ offense showed signs of life on the final play of the third quarter when Smith hooked up with receiver Tyreek Hill for a 38-yard completion down the left sideline giving the Chiefs a fresh set of downs at the Giants’ 16-yard line.

But after two middling plays, followed by a third-down drop by tight end Demetrius Harris on a pass at his feet, the Chiefs were forced to settle for another 31-yard field goal by Butker that knotted the score at 6-6 with 13 minutes, 30 seconds left.

From there, the Giants punted twice and KC once before the Chiefs tried to awaken their dormant offense with a trick play. Facing a second-and-10 at their own 40, the Chiefs dialed up what appeared to be a screen to Kelce who then ran back toward the middle of the field and uncorked a deep ball to receiver Demarcus Robinson.

The Chiefs, however, liked that play against a different coverage. The Giants played a better one, Robinson was bracketed by a pair of defenders, and one of them — All-Pro safety Landon Collins — jumped the route to secure the interception.

The Giants’ offense quickly sputtered afterward, but Brad Wing unleashed a majestic punt that traveled 57 yards and was downed at the Chiefs’ 5-yard line. That actually set up the go-ahead score because Giants cornerback Janoris Jenkins intercepted a throw intended for Robinson and returned it 23 yards to the Chiefs’ 17.

The Giants failed to advance past the Chiefs’ 8-yard line, but kicker Aldrick Rosas connected on a 26-yard field goal that gave New York a 9-6 lead built entirely off three Chiefs turnovers.

“We have to do better than that,” Reid said.

The Chiefs got the ball back with 1:30 left, but disaster appeared to strike again when Smith was again picked by Jenkins for what would have been a game-ending interception.

Jenkins, however, was whistled for defensive pass interference, keeping the drive alive. Smith took advantage.

On the very next play, he connected with Kelce on a 32-yard throw, and a few plays later, he converted a third-and-5 at the Giants’ 29 by weaving through a swarm of oncoming rushers, sprinting toward the sideline and diving over a defender to move the sticks with under a minute left.

The Chiefs settled for a field goal that knotted the score at 9 with one second left. That sent the game into overtime, where the Chiefs got the ball first but failed to do anything with it. The Giants were not as wasteful.

“We could smell it, we could taste it, it was there for us,” Manning said. “And we went and got it.”

After converting three first downs, and facing fourth and 5 at the Chiefs’ 36, Manning (19 of 35, 205 yards) stood in the face of an all-out blitz and attacked cornerback Phillip Gaines. Roger Lewis made a diving catch for a 31-yard gain (despite a pass interference penalty on Gaines) that set up Rosas’ 23-yard field goal to solidify the win.

“It means a lot because it’s against a team that everyone knows is a special team, a playoff-caliber team,” Giants cornerback Dominique Rodgers-Cromartie said.

But while the Giants remain the only NFL team the Chiefs have never beaten on the road, the Chiefs now have more important concerns than history.

After a dynamite 5-0 start that led many pundits to proclaim them a Super Bowl contender, they’ve now lost four of their last five and appear to have multiple flaws, not the least of which is an offense that has essentially gone dormant in all four of its losses and once again failed to deliver on Sunday.

“Plenty of teams have started out hot — you’ve got to continue to get better,” Smith said. “These games get bigger as the season goes on and you have to find a way to win.”