Wesley Skiffington's extra point provided the winning margin for the Seawolves (1-2), who drove 73 yards in 14 plays for the final score.
Coulter was 10-for-12 for 137 yards and the touchdown to Porter. Dayne Hoffman also threw for 59 yards and a score for Stony Brook.
Kyle Newhall-Caballero was 29-for-45 for 267 yards and three touchdowns for Brown (0-1), the defending Ivy League champion.
Newhall-Caballero threw a 20-yard touchdown pass to Matthew Sudfeld, a 23-yarder to Buddy Farnham and a 6-yarder to Alex Prestley, which gave Brown a 20-14 lead with 5:36 left in the third quarter. However, Drew Plichta missed the extra point.
Farnham caught 12 passes for 121 yards.
Miami has lost running back Gus Edwards for the entire season because of a left foot injury.
Virginia Tech will wear a decal on its helmets against No. 1 Ohio State on Monday night to honor slain Roanoke television journalists Alison Parker and Adam Ward.
South Carolina football players will wear stickers on their helmets this season to honor the nine people who died in a shooting at Emanuel AME Church in Charleston this past June.
Washington has found its starting quarterback, but coach Chris Petersen said the Huskies will keep that information under wraps until Friday's season opener at No. 23 Boise State.
Joey Counts scored on a 1-yard run on fourth-and-goal with 2 seconds left to give Montana a 38-35 victory over four-time defending FCS champion North Dakota State on Saturday.
Transfer Vernon Adams will be the starting quarterback when Oregon begins its season against Eastern Washington on Sept. 5.