Mark Jankowski, Anthony Florentino, Shane Luke, and Trevor Mingoia scored for Providence (22-10-6). The Friars led 1-0 after the first, and scored three second-period goals.
Providence is making its 10th tournament appearance, but the first since 2001. It was the Friars' first win in the tournament since 1991.
The Friars will play top-seeded Union on Saturday in the regional championship game. The Dutchmen beat Vermont 5-2 in the first semifinal.
Quinnipiac finished the season 24-10-6. This was in just the third NCAA tournament for the Bobcats, who lost to in-state rival Yale in last year's national championship game.
Quinnipiac's Michael Garteig made 22 saves.