Rice scored seven straight points late in the game and finished with 28, rallying the Illini past Boston University 66-62 on Wednesday night in the first round of the NIT.
"I'm proud of our kids for not getting discouraged when you're on the road and you're down 30-13," Illinois coach John Groce said.
That was the first-half deficit the Illini faced before Rice scored three quick baskets to help them cut the margin to nine at halftime. Rice then made the key play with 2:07 left when his steal and three-point play trimmed it to 61-60. He added two free throws and a driving layup to give Illinois a 64-61 lead.
"My teammates did a great job finding me and putting me in a position to score the ball," Rice said.
Dom Morris missed a contested layup on an inbounds play with 10 seconds left that would have tied it for BU, the regular-season champion in the Patriot League.
"It looked like there was contact, but we didn't lose the game because of that," Terriers coach Joe Jones said.
Nnanna Egwu made two free throws to ice it for second-seeded Illinois (20-14), which advanced to play No. 3 seed Clemson in the second round. Malcolm Hill had 10 points and guard Joe Bertrand, the only senior on the team, added nine.
It was the first meeting between Illinois and BU (24-11), winless in six NIT games. D.J. Irving scored 17 points for the seventh-seeded Terriers, and point guard Maurice Watkins had 12 assists. Morris and John Papale each scored 10.
"They made plays down the stretch and we didn't," Jones said. Irving said guarding Rice was "a difficult task. He's a strong kid and pretty skilled. He took control of the game down the stretch."
After going 1 for 17 on 3-pointers in a blowout loss at home to American in the Patriot League championship a week ago, BU made seven in the first half alone en route to a 33-24 lead at the break.
"They were more intense and played harder than us in the first half," Groce said. "I give them credit. That's a good team."
Illinois shot 58 percent in the second half -- 60 percent on 3s -- and put the clamps on BU's offense late in the game.
"The last 8 minutes of the game, I thought our defense was terrific," Groce said.
The Terriers also went just 5 for 11 at the free throw line.