Forward Chris Baird picked up Coughlin's rebound and slipped it past Bracco, to tie it up 1-1.
The Crimson took the lead at 6:25 thanks to defender Bryan Lonsinger.
His slapshot from the top of the left face-off circle revived the familiar sieve chants among the Crimson fans.
Center Perry Cohagen and Gustafson were credited with assists.
Dartmouth knotted the score at 2-2 at 14:15 on a power play that was a result of defender Matt McCann's roughing penalty.
Big Green center Tom Nieman centered the puck from the bottom of the right circle. From there center Tony Del Carmine slapped it past a screened Hughes. Dartmouth defender Matt Collins tallied an assist.
Ahead for Good
The Crimson reclaimed its lead over the Big Green again on a power play goal at 12:05 in the third period. Center Steve Flomenhoft tipped in a loose puck that slid in from the left side of the crease. Forwards Matt Mallgrave and Tim Burke were there for the assists.
"I'm hoping its a good omen with these power play goals," Tomassoni said. "Its a good sign for the team."
Harvard was two-for-eight on the night on the power play.
Holding a 3-2 lead, the Crimson defense clamped down. Dartmouth got off only one shot on goal in the entire third period.
The Big Green pulled its goalie with 1:30 left in the contest, only to watch Burke securing his team's victory with a last minute empty net tally to put Harvard up 4-2.
"We learned that we can't overlook anyone," Tomassoni said. "Its a sign of a good team that we could come back and get the win."