LAWRENCE — “Big Monday” still belongs to Kansas basketball and head coach Bill Self, but only by an eyelash.

The seventh-ranked Jayhawks rode a 20-point outburst from light-scoring sophomore guard Marcus Garrett and held off a furious late rally from visiting Texas en route to an 80-78 victory at Allen Fieldhouse. Garrett hit a free-throw attempt with five second left, and red-hot Texas guard Jase Febres missed a potential game-winning contested 3-pointer just ahead of the final buzzer to secure the outcome.

The victory pushed Self’s home record with KU in “Big Monday” telecasts to 27-0 and delivered the program a 31st consecutive victory inside “The Phog” on ESPN’s weekly college hoops showcase.

Suiting up for a program rich in remarkable active streaks, any KU player unaware of the history they extended Monday should probably receive a pass. That’s certainly true of junior forward Dedric Lawson, who arrived two years ago as a Memphis transfer.

“I ain’t even know. I ain’t even know,” Lawson said of the “Big Monday” streak. “You know, in Memphis, we didn’t have Big Monday or Terrific Tuesday or whatever they call it. So yeah, I guess it is pretty special to keep doing this.”

It took a pretty special effort just to get past the Longhorns.

The Jayhawks (15-2, 4-1 Big 12) trailed by two at the break despite a committing no first-half turnovers and getting what was already a career-high 17 points and three made 3s from Garrett. The Longhorns (10-7, 2-3) used a late 10-2 run to take the lead and, after surrendering a 3-pointer to Lagerald Vick in the final moments, carried a 40-38 advantage into the locker room.

Febres missed a dunk at the buzzer, and Self gave his guards an earful as they jogged to the tunnel.

“He was pretty upset about not getting back,” recalled Lawson, who finished with 17 points and eight rebounds. “That two points could’ve been maybe the difference in the outcome. Things like that, he pays attention a lot to the small details, and he was pretty mad at the guards for not getting back.”

Whatever message Self delivered at the intermission appeared to work, with the Jayhawks ripping off their own 10-2 run to start the second half in a rally capped by another Vick 3. The teams continued to trade blows until freshman forward David McCormack gave KU an eight-point advantage with a nifty jumper in the paint at the 12:24 mark, forcing a Shaka Smart timeout.

Out of the stoppage, it was Garrett — who else? — whose layup pushed KU’s advantage to double-figures. The 6-foot-5, 195-pound defensive specialist out of Dallas, who is starting in place of permanently sidelined 7-foot center Udoka Azubuike in the Jayhawks’ four-guard lineup, entered Monday averaging 5.8 points on 34.2-percent shooting with an 18.2-percent clip from distance but made 8 of 11 overall attempts against the Longhorns.

“Best defender we have,” Self said of Garrett, “and tonight he was our best offensive player, too.”

But like so many of KU’s opponents across the first five games of conference play, Texas wasn’t going away easily.

The Jayhawk advantage hovered around that double-figure mark until a Jaxon Hayes dunk and Kerwin Roach 3-pointer on back-to-back possessions cut their team’s deficit to five, 69-64, and forced a Self timeout with 4:13 remaining. The Roach trey was the first of the half for the Longhorns — they had been 0 of 8 to that point — but it wouldn’t be their last.

Febres hit three straight 3-point attempts to evaporate the Jayhawk lead, locking the game at 73-all with 2:26 left. But Lawson hit a pair of free-throw attempts, and on the Longhorns’ ensuing possession, Garrett forced a jump ball by creeping up behind Texas’ Dylan Osetkowski, giving possession back to KU. The sequence set up another clutch Vick 3, which pushed his team’s advantage to five with 1:28 on the clock.

“Biggest play of the game,” Self said of Garrett’s tie up with Osetkowski. “That’s what he does, though. You’ve got to have him in the game. He gets the jump ball and we have the possession arrow. That was a huge play there.”

Lawson agreed.

“That was just a smart play from Marcus, defensive instincts kicking in,” Lawson said. “He came over and when (Osetkowski) spinned baseline he had nowhere to go. We knew it was our jump ball — coming out of a timeout Coach had said (that). It was just a smart play by (Garrett).”

Matt Coleman hit a jumper and, after Lawson made one of two free-throw attempts, Courtney Ramey connected on a long 3 to give the Longhorns a chance with nine seconds left. But Garrett hit one of two tries at the stripe, Febres couldn’t connect on a potential game-winning 3 that was contested by Vick at the top of the key, and Quentin Grimes grabbed the defensive rebound to elicit a sigh of relief from Allen Fieldhouse.

“We called timeout and told ’em to definitely try to take away the 3 and switch everything, but no and-1s and guard the 2. So I guess we told ’em to do everything,” Self quipped. “Of course I haven’t seen it, but we defended that well and didn’t let them get off a good look.”

Vick finished with a team-high 21 points, while Dotson (10 points) rounded out the double-figure scorers for the Jayhawks, who committed just four turnovers but made only 11 of 21 attempts from the free-throw line. Coleman’s 16 paced a Texas attack that featured five double-figure scorers and a 13-for-34 team mark from 3-point range.

KU continues conference play with a 1 p.m. Saturday contest against West Virginia in Morgantown, W.Va. Despite just a plus-six-point scoring margin through five Big 12 contests, the Jayhawks will do so with a 4-1 league record.

If the squad is to win a record-extending 15th straight conference championship, it will be because of victories like Monday — “big” victories, if you will.

“That was a heck of a basketball game,” Self said. “That was well-played by both teams.”