The Buckeyes (11-5) will face No. 1 seed Duke (17-1) next Sunday. The Blue Devils advanced by beating Loyola, 12-7.
Ohio State, in its third playoff appearance, will be making its first trip to the quarterfinals.
The Buckeyes jumped out to a 5-1 lead over the Big Red (11-4). They padded their lead to 10 goals four times in the second half , totaling 29 shots, and scored on 11 of 15 shots in the first half.
Ohio State goalkeeper Stefan Schroder (nine saves) went the length of the field to score the first goal at the 11:32 mark of the first quarter. John Glynn, Ryan Hurley and Max Seibald all scored twice for the Big Red. Glynn also had two assists and won 13 of 19 faceoffs.
Both teams went scoreless for more than eight minutes in the fourth quarter.
Ohio State 5 6 2 2 - 15
Cornell 1 1 2 3 - 7
Goals: OS-Poillon 3, Buchanan 2, Dalgarno 2, Green 2, Friel 2, Lathrop, Pages, Ryan, Schroder; C-Glynn 2, Hurley 2, Seibald 2, Calvert. Assists: OS-Dalgarno 2, Buchanan; C-Glynn 2, Espey, Finn, Hurley, Moyer. Saves: OS-Schroder 9, Freeman 0; C-Harer 5, Martinez 2, Myers 0.