LUBBOCK, Texas -- No. 3 Kansas was pitted in a nail-biter Saturday and playing without go-to standout Frank Mason, a candidate for national player of the year.

The senior guard fouled out with 3:05 remaining after playing through an illness and managing 12 points, eight fewer than his Big 12-leading average, on 4-of-13 shooting.

Freshman guard Josh Jackson took over, though, hitting the decisive free throw with 2.8 seconds remaining to finish with a career-high 31 points as the Jayhawks nipped Texas Tech 80-79 in United Supermarkets Arena.

"With Frank under the weather, he's been a little sick, and him fouling out,'' Jackson said, "I knew I had to make a couple of extra shots.''

Jackson actually did more than that, adding a game-high 11 rebounds and recording his fourth double-double in five games. It was the third time in six games Jackson led the Jayhawks (22-3, 10-2 Big 12) in scoring, making it easy for Kansas coach Bill Self to set up the last play after timeouts were called by both teams with 5.3 seconds left.

"We said, 'Just give it to Josh and get out of the way,''' Self said. "He played great. It was probably his most complete game he's had since he's been here and on a night when Frank was off.''

Not everyone cleared out, however, and senior forward Landen Lucas set a crucial pick, which enabled Jackson to get enough clearance to launch his drive just inside the top of the key before drawing a foul from Texas Tech junior forward Zach Smith.

"The play that really made the game was the screen Landen set to get me open,'' Jackson said.

Texas Tech (16-9, 4-8) grabbed five leads in the second half and remained within striking distance, but did not score after Smith connected with 1:15 remaining.

The Jayhawks did not immediately capitalize. Lucas, who added 13 points, missed the front end of a one-and-one with 59 seconds left and Jackson did the same with 38 seconds left.

However, Texas Tech junior guard Niem Stevenson committed an unforced turnover and senior forward Aaron Ross missed a 3-pointer as the game remained tied at 79.

"I thought in the second half we competed and we outplayed Kansas,'' Texas Tech coach Chris Beard said. "In this game we probably outplayed them 28, 30 minutes of the 40. What matters is the final scoreboard.''

Junior guard Keenan Evans scored 25 points. Stevenson added 21. They came in averaging 14.4 and 7.2 points respectively. Stevenson also snared 10 rebounds along with Smith, who added 21 points.

The Red Raiders trailed by as many as 12 in the first half but still threw a scare into the Jayhawks, who retained their one-game lead in the Big 12.

"Our fans getting into it, giving us support was big,'' Evans said of Texas Tech's first sellout on the season. "Everybody was talking together and playing as one, helping each other out, and just getting better offensive looks on the other end in the second half.''

Graham added a game-high six assists for Kansas.

Jackson paced the Jayhawks in the first half with 13 points and six rebounds as the Jayhawks opened a 42-35 lead at the break. Lucas and junior guard Svi Mykhailiuk added nine points apiece.

The Jayhawks used a 6-0 flurry capped by a 3-pointer from Mykhailiuk to gain their largest lead of the half, 34-22, with 4:23 left. The run was part of an onslaught in which Kansas made 5 of 6 shots.

A bucket by Smith allowed the Red Raiders to crawl within 40-35 before a layup by the Jayhawks' Carlton Bragg capped the first-half scoring.

Evans kept the Red Raiders within striking distance with 17 first-half points and 6-of-7 shooting. Stevenson added eight points.

NOTES: Earlier in the week, Kansas coach Bill Self attended a high school game played by five-star recruit Trae Young of Norman, Okla. Young's father, Rayford, played for Texas Tech. Young scored 62 points in a game he played Friday for Norman North High School. He is expected to announce his decision on Thursday. Kansas, Oklahoma and Oklahoma State are considered the finalists. ... Kansas drew a No. 1 seed in the Midwest Region and the overall No. 2 seed during a pre-NCAA Tournament selection show that aired Saturday. Big 12 rival Baylor was the No. 3 overall seed. Villanova and Gonzaga also were slotted on the one-seed line. ... Texas Tech's Chris Beard came in ranked eighth among first-year Division I head coaches for 2016-17 in victories (16). The leader was Paul Weir of New Mexico State (22). ... Kansas won its 16th straight in the series and seventh straight at Texas Tech.