SAN ANTONIO - As hard as it is to imagine, Memphis keeps getting better just when it matters the most.

The Tigers claimed their piece of history Saturday, beating UCLA 78-63 in the NCAA men’s semifinals to become at 38-1 the winningest team ever in a single season. Now they have a chance to do what the other 37-win teams — Duke, Illinois and UNLV — couldn’t do: cap it off with a national championship.

With Derrick Rose and Chris Douglas-Roberts taking turns at basketball acrobatics, it’s certainly imaginable. And the Bruins certainly wouldn’t doubt it.

“Going into the game, we knew that we was going to win. Ain’t too much to say,” Rose said. “We’re just a great team. With the team that we have, it’s hard beating us.”

Coach John Calipari claimed his Tigers weren’t aware they had set a record for most wins in major college basketball.

“My team’s like, ’Is it? That’s the most wins?”’ Calipari said. “And then I told them, ’No, no. You’ve got to get to 39 to have the most wins.’ Hopefully we’ll have one more in us.”

The Tigers will get their chance Monday night against Kansas, which beat North Carolina 84-66.

All season, this Memphis team from lightly regarded Conference USA played along with Calipari’s us-against-the-world theme. Now, the Tigers need only one more victory for their first championship.

UCLA star Kevin Love put on his own show at practice Friday, hitting a full-court shot. He managed just 12 points — and missed both open 3-pointers — as the Bruins (35-4) again fell short in their third straight Final Four appearance.

“As disappointing as this loss is, it’s hard to be here three years in a row and not come away with a championship,” coach Ben Howland said.

“You have to give credit to Memphis State,” he said. “There’s a reason why they’ve only lost one game and they’ve won 38. They’re a very, very good team.”

Rose and Douglas-Roberts, especially.

A star freshman, Rose wasn’t content to merely make shots, he wanted to stamp this Final Four as his own with a series of show-stoppers that became an NBA audition.

Rose put up lefty floaters and righty scoops, often changing hands in mid-air, and threw one try over his shoulder. He was in perpetual motion — once, he caught a pass in traffic, stutter-stepped just long enough to look his defender in the eye, and then sped past him for an easy but showy layup.

“Every once in a while, I go, ’Oh my’ and I kind of sit down,” Calipari said. “And they usually come at inopportune times for the other team.”

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Rose finished with 25 points and nine rebounds and a bunch of eye-opening moves that won’t show up in the final box.

Rose also hit 11 of 12 free throws. For a team supposedly vulnerable from the foul line, the Tigers did great in making 20 of 23.

He fittingly wound up with the ball in the final seconds and heaved it high. Only then did he crack the slightest of smiles.

Douglas-Roberts played like an All-American, scoring 28 points and Joey Dorsey had the most peculiar line of all — zero points, but 15 big rebounds in keeping Love out of the middle.

“It’s great, it’s great,” Douglas-Roberts said. “We all believe in each other and we expect great things to happen, so this isn’t new to us.”

Four other teams had won 37 times in a season — Illinois in 2005, UNLV in 1987 and Duke in 1999 and 1986 — but all lost in the end.

Memphis has won its five games in this NCAA tournament by an average of nearly 16 points. The Tigers got off to a slower start this time, falling behind 5-0, before their suddenly chic “dribble drive motion” offense took over.

Memphis led 50-45 with 13½ minutes left before pulling away. Rose made a couple of nifty passes, Dorsey came up with a monster block and later playfully popped Douglas-Roberts on the shoulder after a slam.