Travis Warech missed a fallaway with a couple seconds to play, but the ball bounced out directly in front of the rim and Maravich just got a finger on the ball a few tenths of a second before the horn sounded.
Rochester led by as many as eight in the second half, but Ithaca used an 8-1 spurt to get back within one at the eight minute mark.
The Bombers finally tied the game with three minutes to go on a Frank Mitchell layup and took the lead when Warech hit 43 seconds later.
Nate Vernon quickly tied it for the Yellowjackets, but Mitchell made another layup with just under two minutes remaining to put Ithaca up 68-66.
Rob Reid made two free throws to tie with 93 seconds left. Each team then drained the shot clock, only to miss three pointers. The Bombers ended up with the ball in a tie game and 30 seconds to go, allowing them to call time out and hold for the last shot. The plan worked, though certainly not as expected.
Ithaca now qualifies for the Sweet 16 for the first time in school history. Rochester finishes its season 22-5.