Whyte blocked a Cornell shot from the point, took the puck end to end and beat Toth with a shot to the upper corner.
With a 2-0 lead, Harvard again found itself under seige by the Cornell attack.
The Big Red received a power play in the closing minutes, but could not convert as Harvard escaped with a shutout.
While the win only moves Harvard to the middle of the league standings, a berth in the ECAC Tournament is not out of the question.
Dooley sees improvements in this young team, particularly in the play of freshman defenders Diana Clark and Winkie Mleczko.
With its new-found momentum, Harvard is looking to avenge earlier losses to league-leaders Dartmouth and Princeton.
Dooley concedes, however, that the Crimson needs to be nearly perfect for the rest of the season.
"We've got to pretty much win all of our Ivy games to make the tournament," Dooley said.