Fellow senior Eric Paschell added 14 points for the sixth-seeded Wildcats, who led for almost 33 minutes, but never by more than eight points.
Jordan Ford and Malik Fitts each had 13 points for Saint Mary's, which finished the season 22-12. The 11th-seeded Gaels, who pulled off an upset win over Gonzaga in the West Coast Conference Tournament, had a chance down the stretch in this one.
Ford's basket in the lane after a few nifty moves got the Gaels within six points at 61-55 with 34 seconds left. After Paschell missed a foul shot on the other end, Fitts cut the deficit to four points with a leaner in the lane.
The Gaels had two more chances in the final seconds after a foul by Booth and some missed free throws. But Fitts hit the rim on a 3-point attempt and Saddiq Bey stole the ball from Ford in the final seconds to seal the win.
Saint Mary's led 30-28 at the half, but Booth scored the first five points after intermission, part of a 12-3 run that put the Wildcats up 40-33.
The third-seeded Boilermakers (24-9) will play reigning NCAA champion Villanova, the sixth-seed in the South Region, on Saturday.
Edwards, the Big Ten's leading scorer, has been slumping recently and dealing with a sore back that he insisted was fine on Wednesday. The junior guard had shot 32 percent in his last 11 games, and was 7 for 33 from 3-point range in his last three games.
Ahmad Caver scored 19 points and B.J. Stith had 14 for Old Dominion (26-9). The Monarchs shot 27 percent from the field in their first NCAA appearance since 2011.
The Boilermakers scored the last 11 points of the second half as ODU went stone cold. The Monarchs missed their last 11 shots of the half and went scoreless for 6:17 as Purdue took a control and led 32-19 at the break.
It got no better for the Monarchs in the second half. Matt Haarms, Purdue's 7-foot-3 center made a 3 from the corner to make it a 17-point game with 16:50 left in the second half. It was Haarms' seventh triple of the season. A minute late, Edwards pulled up for a long 3 that made it 43-23 and prompted ODU coach Jeff Jones to call a timeout.
The lead was 17 with 7:13 left when ODU went on a 12-4 run. Xavier Green's running hook over Haarms cut the lead to 55-46 with 4:23 remaining. But it never got any closer.
All times Pacific, with TV (*approximate time; game will start 30 minutes after the completion of the previous one):
at Columbus, Ohio
7 Cincinnati (28-6) vs. 10 Iowa (22-11), Channel 2, 9:15 a.m.
2 Tennessee (29-5) vs. 15 Colgate (24-10), Channel 2*, 11:45 a.m.
at Columbia, S.C.
8 Mississippi (20-12) vs. 9 Oklahoma (19-13), TruTV, 9:30 a.m.
1 Virginia (29-3) vs. 16 Gardner-Webb (23-11), TruTV*, noon
at San Jose
4 Kansas State (25-8) vs. 13 UC Irvine (30-5), TBS, 11 a.m.
5 Wisconsin (23-10) vs. 12 Oregon (23-12), TBS*, 1:30 p.m.