After the Scarlet Knights took a 34-30 lead on Janarion Grant's 55-yard punt return for a touchdown with 1:31 left, the Cougars (1-1) drove 90 yards on 10 plays in 1:18 to retake the lead.
Falk, who threw four touchdowns and 478 yards, threw a lob in the back of the end zone for Cracraft, who leaped and cradled the ball for a three-point lead.
The Scarlet Knights took a 27-23 lead on Grant's 100-yard kickoff return for a touchdown, but trailed 30-27 after Falk threw a 23-yard touchdown pass to Gabe Marks, who had 14 catches for 146 yards, with 9:31 to play.
After the Cougars punted, Grant caught the punt and broke free down the right sideline to give Rutgers a four-point lead.
Chris Laviano threw 204 yards, one touchdown and one interception, and also lost a fumble. Josh Hicks ran for 91 yards, but had a 21-yard touchdown run called back with a holding penalty. On the ensuing play, Hicks lost a fumble after catching a screen pass.
Grant also had a receiving touchdown wiped when Justin Goodwin was called for offensive pass interference.
The Scarlet Knights trailed 20-6 midway through the third quarter, but tied the game on a Robert Martin 15-yard touchdown run and Laviano's one-yard touchdown pass to Matt Flanagan with 14:56 remaining in the game.
Washington State's Erik Powell kicked a 37-yard field goal to take a 23-20 lead, but Grant returned the ensuing kickoff 100 yards for the touchdown.
Falk threw a seven-yard touchdown pass to Dom Goodwin in the first quarter and a six-yard touchdown pass to Keith Harrington in the third quarter.
The Scarlet Knights travel to Penn State for their first road game on Sept. 19 at 8 p.m.