Third-seeded Nevada (21-12) will play at Rhode Island in the second round.
"From what little we know about the Missouri Valley Conference, it's known for physical defense," said Babbitt, who set Nevada's single-season scoring record during the game. "Wichita State is definitely a physical team, and we did a good job of keeping our cool and playing our game."
Toure Murry scored 15 points to lead Wichita State (25-10), which suffered its first loss in 18 home games this season.
After Wichita State cut the lead to 42-40 on Gabe Blair's dunk, Nevada found its offensive stride again, highlighted by 6-foot-4 Brandon Fields going right at Wichita State's 7-foot center, Garrett Stutz, and throwing down a huge slam. Seconds later, two free throws by Babbitt gave the Wolf Pack a 59-49 lead with 10:33 remaining.
"Brandon's dunk was definitely huge," said Nevada's Armon Johnson, who scored 15 points. "We were already motivated, but when he did that to that big tree, it gave us a boost."
Wichita State was still down nine with 6:20 remaining when it scored eight straight to make it 66-64 with 4:26 left.
It was still a two-point game when Babbitt hit the biggest shot of the night, getting off a 17-footer a fraction of a second before the shot clock expired and sinking it for a 72-68 lead with 33 seconds remaining.
Wichita State's Clevin Hannah scored on a layup with 24.2 seconds to play, cutting the advantage to 72-70, but Babbitt hit two free throws for the final margin.
"We just had some bad performances," Wichita State coach Gregg Marshall said. "We had some guys not handle the (10-day) layoff very well."
Nevada was able to stymie Wichita State's offense for most of the first nine minutes, taking a 14-7 lead while holding the Shockers to 3-of-13 shooting. But Wichita State started to put it together after that and climbed back in the game. The Shockers made seven of eight shots during a 17-5 run that included three baskets by Murry and led 24-19.
Three-pointers from Nevada's Ray Kraemer and Fields helped the Wolf Pack close the deficit, and the score was tied at 31 at halftime.