Now, the Bears (27-7) head back to their home state to play 10th-seeded Saint Mary's in Houston in the round of 16.
Baylor struggled to beat Sam Houston State in the first round for its first NCAA tournament win since 1950, but the Bears arrived loose and confident against Old Dominion, taking a double-digit lead amid a barrage of early 3-pointers and alley-oops.
After the Monarchs (27-9) rallied to take the lead in the second half, Baylor received a big lift from 7-footer Josh Lomers, who tied a career high with 14 points, 12 in the second half.
Old Dominion, which edged No. 6 seed Notre Dame 51-50 in the first round, was trying to become the first team from the Colonial Athletic Association to reach the round of 16 since George Mason's Final Four run in 2006. The Bears would have none of it, scoring the most points of any Monarchs opponent all season.
Down 38-28, Old Dominion scored nine straight points to start the second half. Frank Hassell dunked to make it a one-point game, then shot the Old Dominion cheering section a quick glance before heading back on defense.
A little while later, Kent Bazemore's two free throws put Old Dominion ahead 49-47 -- its first lead since 1-0.
The Monarchs could never shake the Bears, though, and they couldn't contain Lomers, the lumbering senior who always seemed to be around the basket with the ball. With Baylor ahead 62-61, Old Dominion lost track of Lomers, and his three-point play started the Bears' final big run.
Dunn's 3-pointer made it 68-62, and a reverse layup by Tweety Carter put Baylor ahead by eight.
Hassell had 15 points and eight rebounds for Old Dominion.
The Bears made their first four shots of the game -- including 3-pointers by Dunn and Carter and an alley-oop from Carter to Dunn -- to take a 10-1 lead. Bazemore answered with an alley-oop dunk of his own at the other end, but that did little to stem the tide. Dunn made a 3-pointer and sneaked behind the defense for another alley-oop from Carter for a 15-5 lead.
Baylor led by as many as 14, and yet another alley-oop -- again Carter to Dunn -- made it 31-18. Carter capped the half with a floater that beat the buzzer to make it 38-28.
Carter finished with 12 points and eight assists.