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.
Mississippi State freshman guard Malik Newman will withdraw from the NBA draft, but sources told ESPN he might explore other opportunities besides returning to Mississippi State.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.