The Eagles (1-3) were off to their worst start since opening 1991 with four losses under then-coach Tom Coughlin.
Kevin Pierre-Louis returned a fumble 96 yards for a TD and Nick Clancy had one of 16.
Jesse Julmiste had a 100-yard kickoff return for a score for the Minutemen, and Jonathan Hernandez carried 22 times for 80 yards and a TD.
Massachusetts (2-1), a Football Championship Subdivision school, is making the first of a two-year jump into the Football Bowl Subdivision. The Minutemen will be part of the Mid-American conference in 2013.
It was the 24th meeting between the schools, dating back to the first in 1899. BC leads 19-5, winning its seventh straight.
Rettig completed 14 of 22 passes for 196 yards with the three TDs and no interceptions. Andre Williams carried 20 times for 95 yards and last season's Atlantic Coast Conference leading rusher Montel Harris returned from preseason left knee surgery and ran nine times for 27 yards.
Colin Larmond Jr. had two TD catches — 36 and 37 yards — and backup running back Tahj Kimball had a 3-yard run for a score.
The Eagles' Hampton Hughes picked off UMass quarterback Kellen Pagel on the first offensive play of the game, giving BC the ball at UMass' 47. Eleven plays later, Rettig hit tight end Lars Anderson with a 1-yard score to give BC a 7-0 lead.
After a short drive by the Minutemen, the Eagles took over on their own 45 and marched to the UMass' 8 before the stalling. Nate Freese booted a 26-yard field goal, making it 10-0.
Things weren't going very well early offensively for the Minutemen. Rettig had as many completions (six) as UMass had offensive plays late in the opening quarter.
BC took over in UMass territory early in the second quarter after a short punt gave them the ball at UMass' 44. Kimball ran in from the 3 five plays later, making it 17-0. Rettig hit Johnathan Coleman for a 24-yard strike on the prior play.
Julmiste took the ensuing kickoff a couple of steps in his own end zone, broke free up the left sideline for his score, making it 17-7. NCAA statistics only list returns of 100 yards despite Julmiste taking the ball back about 102.
But BC struck back on its next offensive series. Rettig hit a wide-open Larmond Jr. along the left sideline for a 36-yard score, capping a 54-yard drive that took seven plays and increased the lead to 24-7.
The Eagles, coming off a heartbreaking 20-19 loss at home to Duke last week when Freese hit the left upright with a potential game-winning field goal in the closing minute, dominated on the scoreboard, statistics and time of possession in the opening half. The Eagles doubled UMass in total yardage and held the ball nearly 21 minutes to just over nine for the Minutemen.
Brendon Levengood kicked a 38-yard field goal, cutting BC's lead to 24-10 late in the third quarter.
Larmond Jr.'s second TD of the game — a leaping 37-yarder in the left side of the end zone — made it 31-10. Clancy picked up Hernandez's fumble and ran in untouched for a score on the next series.