Costello finished with eight receptions for 121 yards. He caught scores of 49 and 17 yards from Michelsen to push Princeton (3-2, 2-0 Ivy) out to a 24-0 lead in the second quarter.
Brown (2-3, 0-2) clawed into the deficit with three field goals by Grant Senne. Marcus Fuller's 20-yard touchdown pass to Brian Strachan pulled the Bears within 9, but Brown's ensuing drive stalled at their 27.
Fuller threw for 454 yards on 29-of-71 passing with a touchdown and two interceptions. Troy Doles had 200 yards on six receptions and Strachan had 146 on 10.