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.
Udoh also had five assists, two blocks and two steals for the third-seeded Bears (26-7), who broke open a close game down the stretch to earn their first NCAA tournament win since beating BYU in 1950.
LaceDarius Dunn scored 13 points for Baylor. 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 to put Baylor ahead for good with 2:30 left.
Acy and Anthony Jones both finished with 10 points for Baylor.
Sam Houston State, normally a strong 3-point shooting team, was undone by misses from long range, going 6 of 31.
The game was a homecoming of sorts for Mitchell and Baylor point guard Tweety Carter, who grew up as friends in the New Orleans area. They didn't stand out in this game, however. Neither even scored in the first half.
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. Baylor moves on to play Saturday against 11th-seeded Old Dominion, a 51-50 winner over No. 6 seed Notre Dame earlier Thursday.
Back in the tournament for the second time in three seasons, Baylor nonetheless seemed plagued by first-round jitters early on, starting 1 of 4 from the field and committing several turnovers.
It was just the opposite for Sam Houston State's Preston Brown, who scored his team's first eight points. Clavell then dunked for his first points, making it 10-3 and giving the BearKats the largest lead either team enjoyed in a tight first half.
The BearKats, who'd hit as many as 18 3s in a game at Kentucky this season, struggled early from long range, going 2 of 16 in the first half.
Clavell made up for it, matching his season average of 17 points within the first 20 minutes.
Udoh scored 10 points in the first half, with his free throws pulling Baylor to 31-30 at halftime.