Rosenberg had 20 points and Mullins added 19 with Lo Maodo contributing 12 and Isaac Cohen 10.
Columbia (12-6, 1-0 Ivy League) led 29-26 at the half. The Lions went on a 16-4 run to open the second period to lead 45-30 with 14:33 remaining. Cornell (1-14, 0-1) did make a run late and closed to 67-60 with 54 seconds remaining. Rosenberg and Mullins made four consecutive free throws to close out the scoring.
Columbia pulled down 32 rebounds compared to 24 for Cornell. The Lions shot 47.6 percent from the field while Cornell managed 39.6 percent.
Forward Kennedy Meeks, who has averaged 9.4 points and 6.5 rebounds at North Carolina, has pulled out of the NBA draft and will return to the Tar Heels.
Cal big man Ivan Rabb could have been selected in the top 10 of the NBA draft. Instead, he's returning to Berkeley to make himself, and the Golden Bears, stronger.
Devin Williams' decision last month to sign with an agent and enter the NBA draft has left West Virginia in a tough spot.