LAWRENCE, Kan. -- Now comes the tough part for the Kansas Jayhawks.

Second-ranked Kansas overcame a huge game from Texas freshman Jarrett Allen on Saturday, outlasting the Longhorns, 79-67, for its 18th straight victory.

The victory kept the Jayhawks (18-1 overall, 7-0 Big 12) atop the conference standings, but up next for the Jayhawks will be a Murderer's Row stretch of high-profile games -- Tuesday at No. 7 West Virginia, followed by a Saturday road game at No. 5 Kentucky and Feb. 1 home game against No. 6 Baylor.

"You can add a couple other games to that -- Iowa State (home game) and at Kansas State," said KU head coach Bill Self. "That stretch is as tough as we've had since I've been here."

Allen, a 6-foot-11 power forward who chose Texas over Kansas in last year's recruiting war, was tough on the Jayhawks as well, scoring 22 points and grabbing 19 rebounds.

"There's a reason why we wanted him," Self said. "To come in here as a freshman and have 22 and 19 ... his length makes it tough. He's a terrific talent."

But, Allen's big game wasn't enough to overcome Kansas' balanced scoring. Devonte Graham led the way with 18 points, Frank Mason scored 17 points, freshman Josh Jackson had 15 and Svi Mykhailiuk added 12 for KU, which shot 54 percent from the field in the second half.

"Kansas had an answer every time and that's what great teams do," said Texas coach Shaka Smart, whose team dropped to 7-12 overall and 1-6 in Big 12 play.

Landen Lucas, despite being ill, played 31 minutes and helped Kansas to a 40-33 advantage on the boards with 14 rebounds.

Kansas had got off to slow starts in its last three games at home, but that was not a problem on Saturday. Graham and Mason knocked down back-to-back 3-pointers to start the game and the KU led 14-2 after six minutes as Texas turned the ball over six times.

But, as has been their habit in recent games, the Jayhawks let Texas back in this one. Mason picked up his second foul at the 10-minute mark and the Longhorns went on a 9-0 run to make it a 24-21 game at the 6:27 mark. The teams combined for 18 turnovers in the first 12 minutes before KU took an eight-point lead into the locker room at halftime.

Texas hung tough for much of the second half and trailed by only seven points with two minutes remaining, but back-to-back 3-pointers by Graham and Mykhailiuk put the game away.

"That's the best we've started in the last few games, but then we had some breakdowns on defense and gave up some easy shots," said Mason, who scored 12 of his 17 points in the second half. "We're going to have to do a better job with that."

Allen played 34 minutes for Texas, hitting 9 of 14 shots from the field and 4 of 7 free throws. Andrew Jones came off the bench to score 15 points, Eric Davis had 12 and Shaquille Cleare added 11. But, the Longhorns turned the ball over 19 times and shot just 37 percent from the field in the second half.

"I thought our guys really responded well and showed a lot of fight today," Smart said. "But, I thought Mason and Graham were awesome the way they controlled the tempo of the game."

The victory was the 54th straight at home (51st in Allen Fieldhouse) for the Jayhawks. Three of those wins have come at the Sprint Center in Kansas City.

NOTES: The Jayhawks have owned the series with Texas since 2008, winning 17 of 20 games, including 11 of their last 12 and six straight. ... Kansas senior Frank Mason is having an All-American-type season, ranking first in the Big 12 in scoring and 3-point shooting, and fourth in assists. ... The Jayhawks have lost only five home Big 12 games in Bill Self's 13 1/2 seasons and have started the season 18-1 six times. ... Texas is 0-8 in games played away from Austin this season.