The Tigers (10-3) will meet unbeaten and No. 19-ranked Central Florida in Thursday's final.
Chaisson Allen led Northeastern (4-7) with 19 points.
After battling evenly for the first 25 minutes, Princeton broke a 31-31 tie with an 18-2 run to lead 49-33.
Northeastern rallied behind Allen, whose 3-pointer cut the deficit to 56-50 with 4:39 to go.
Maddox momentarily stopped the rally with a layup, but Allen wasn't done. His driving layup with 14.5 seconds to play capped a 7-0 run and cut Princeton's lead to 64-63 with 14 seconds left.
Mavraides made 1 of 2 free throws with 13 seconds to play to make it 65-63 and Northeastern's Joel Smith missed a driving layup at the buzzer.