"Sorry I'm late. We haven't won a tournament game in a long time," Drew said. "I know there are happy players in there."
Udoh had 20 points and 13 rebounds, and Baylor dominated the last three minutes of a 68-59 victory Thursday in the first round of the South Regional.
"Oh, man, just joy in my heart, man," Udoh said. "But, whew, that was close. Sam Houston, that's a great team. ... It's tourney time. You've just got to be ready."
Udoh also had five assists, two blocks and two steals for the third-seeded Bears (26-7), who were tied with less than 4 minutes remaining before pulling away for their first NCAA tournament win since beating BYU in 1950.
Baylor moves on to play Saturday against 11th-seeded Old Dominion, a 51-50 winner over No. 6 seed Notre Dame earlier Thursday.
"Really, the game was pretty simple: Get the ball to Ekpe," Drew said. "He's got 20 and 13, 9 for 16 (shooting), let him either create for somebody or let him score. When we did more and more of that, things got easier and easier."
LaceDarius Dunn scored 13 points for Baylor, 10 in the second half. His short, spinning fade and one-handed jam fueled a late 8-0 run that clinched it.
Gilberto Clavell had 23 points and Preston Brown added 13 for 14th seed Sam Houston State (25-8), which tied it at 55 on a short floater by Ashton Mitchell with 3:48 to go.
The game remained tied until Quincy Acy dunked with 2:30 left to spark Baylor's decisive surge and put the Bears ahead for good.
"We knew once Quincy got a dunk or did something crazy on the floor, it would get all of us going," Dunn said.
Acy and Anthony Jones both finished with 10 points for Baylor.
Sam Houston State kept the game close with a triangle-and-two zone defense that BearKats coach Bob Marlin installed with idea of keeping the ball away from Baylor's explosive backcourt of Dunn and Tweety Carter. It worked for most of the game.
"We had the game right where we wanted it with 4 minutes to go and had the basketball, had an opportunity to get a lead, and it didn't happen," Marlin said. "Our defensive game plan was good the entire ballgame. Our guys fought hard."
Baylor players said they were unfamiliar with the triangle-and-two -- effectively man-to-man coverage on the guards and a zone inside -- and had trouble adjusting.
"We were just shocked. We never faced nothing like that," Dunn said. "When we got out there and faced them we were like, 'Wow, what are we going to do?' So it just took us time to calm down."
Yet, even when Baylor struggled, Sam Houston State was unable to pull away. Normally a strong 3-point shooting team, the BearKats were undone by misses from long range, going 6 of 31.
"We did not shoot the ball very well today, especially from 3-point range, and we knew we were going to have to," Marlin said.
Drew praised Sam Houston State's defense, then added, "The story, though, was our defense."
"They're a tremendous offensive team ... had 18 3s against Kentucky, 15 3s against Auburn, and we hold them to six and 33 percent shooting," Drew continued. "So clearly our defense won us the game."
The game was a homecoming of sorts for point guards Mitchell and Carter, who grew up as friends in the New Orleans area. They didn't stand out in this game, however. Neither scored in the first half, which ended with Sam Houston State clinging to a 31-30 lead.
Mitchell, who came in averaging 12.7 points, didn't score until hitting a 3 early in the second half. He finished with five points and six assists.
Carter, who came in averaging 15.7 points, got his only points on a fast-break layup in the second half and had two assists.
Carter will get another chance, though, on Saturday against Old Dominion.