LAWRENCE, Kan. -- Nobody else was doing much scoring for No. 10 Kansas on Monday night. Nobody else was rebounding or playing much defense, either.

Jeff Withey stepped up and did all three.

And etched his name in the school's record books, too.

The senior center had 16 points, 12 rebounds and a school-record 12 blocks for only the second triple-double in Kansas history, and the Jayhawks held off a furious comeback by San Jose State for a 70-57 victory.

"He was the only guy who played worth a flip," Kansas coach Bill Self said. "He did a good job covering up for a lot of mistakes, because we made a ton of them tonight."

Withey scored 10 points during a 20-2 run early in the second half, and achieved the Jayhawks' first triple-double since Cole Aldrich in an NCAA tournament game against Dayton in 2010 when the 7-footer blocked Xavier Jones' shot with 7:43 left in the game.

"I've been wanting that for a while now, and it's only me and Cole that have it, so it's pretty special to me," Withey said. "They kept on driving in and, you know, I just kept on blocking it. It's what I do."

Kansas (5-1) certainly needed every last one of them after taking a 60-36 lead with just over 11 minutes left, and then watching the Spartans (2-3) go on an 18-2 run of their own.

The Jayhawks finally put it away when Elijah Johnson hit a floater with just over a minute left for a 66-57 lead, and when Withey's rejection of D.J. Brown turned into a run-out that Ben McLemore finished off with a windmill dunk with about 30 seconds remaining.

"We didn't back down," San Jose State coach George Nessman said. "We kept bucking up and sticking our chest out there, and that was important for us."

James Kinney stuck his chest out the farthest, scoring 19 of his 30 points in the second half for the Spartans. At one point, the senior guard scored nine in a span of about 90 seconds as San Jose State was mounting its big second-half charge.

"I wasn't going to give up. I'm not going to get embarrassed out here," Kinney said. "Once everyone saw I was going to keep fighting, they just tagged along."

McLemore finished with 13 points despite missing all seven of his 3-point tries, and Travis Releford also had 13 points for the Jayhawks. Kevin Young added eight rebounds.

Playing its first game since romping to victory in the CBE Classic last week, the Jayhawks looked fresh and smooth in building a double-digit lead late in the first half.

San Jose State answered with nine straight points spanning halftime to get back into it.

That's when Kansas went on its big run.

It began with a 3-pointer by Johnson, and the momentum really started to build when Young followed up Withey's miss with an easy basket down low.

Withey scored six of the Jayhawks' next eight points as the lead slowly grew, and the crowd at Allen Fieldhouse began to realize that he was making history. He surpassed the 10-rebound mark midway through the second half before getting his 10th block to mark the triple-double.

"Most of the time -- I'm guilty of it, too -- we get caught standing around watching Jeff, like a fan or something, and that's when we need to snap back to it," Johnson said. "Jeff saved us a lot of times. There were times I caught myself looking instead of playing."

Unofficially, it was Withey's second time reaching the milestone.

The senior had 18 points, 12 rebounds and 10 blocks against Pittsburg State in an exhibition game last season, when All-America forward Thomas Robinson missed the game due to injury.

It also comes with an asterisk in the Kansas record books.

The school didn't keep records for blocked shots during the 1950s, when Wilt Chamberlain was plying his trade on the hardwood. He undoubtedly had his share of triple-doubles while playing for the Jayhawks -- but officially, only Aldrich and Withey have done it.

"On the sideline, I kept thinking some of the shots were going in, and then bang, they were going the other way," Nessman said. "We try to tell our guys to jump into shot-blockers, but he's so good at staying down, it's hard to get him off his feet."

Kinney did the best job of getting shots up, over and around him.

In doing so, he nearly stole Withey's thunder.

The spunky guard hit consecutive jumpers to end the Jayhawks' big second-half run, and then added a fall-away 3-pointer with just over 10 minutes remaining to close the gap.

He added another 3-pointer with 6:44 left to trim the Spartans' deficit to 60-51, and then hit his fourth 3 as the shot clock was winding down to make it 64-57 with 2:39 to go.

That's when Kansas finally put the game away.

"I just don't think we have any fold in us. That's not who we are. We have a great group of kids," Nessman said. "We came here to play for a full 40 minutes."