Zach Auguste added 10 points for the Fighting Irish (14-12, 5-8 Atlantic Coast Conference) in their first road victory of the season. Notre Dame had lost five of its last seven games and was 0-6 away from home.
The Eagles have lost eight of nine and their only two conference wins this season are against last place Virginia Tech.
The Fighting Irish were clinging to a lead late in the game when Connaughton nailed both ends of a 1-and-1, scored on a drive in the lane and hit a short one-handed flip shot in the lane as they held off BC.
The Eagles had sliced Notre Dame's lead to four points three times before Connaughton's timely scoring.
After Connaughton's flip in the lane made it 63-57 with 3 1/2 minutes left, Rahon hit two free throws for the Eagles. But Auguste nailed a short jumper and Knight had a putback, making it 67-59 with 59 seconds left.
Atkins' 3-pointer in the final seconds of overtime lifted Notre Dame past BC, 76-73, in the schools' other meeting in South Bend, Ind. on Feb 1.
The Fighting Irish led by three at intermission and pushed it to 45-38 on Auguste's dunk with just over 17 minutes to play, but BC scored the next seven points with Anderson starting the spurt with a pair of baskets in the lane.
Notre Dame led 38-35 at halftime.
There was a pregame video tribute and moment of silence for longtime BC men's basketball sports information director Dick Kelley, who passed away Thursday night at 48-years old after a battle with amyotrophic lateral sclerosis (ALS). All of the school's sports teams are wearing black patches with white letters "DK" in his memory. Eagles coach Steve Donahue had a patch on his dress shirt.
Notre Dame plays the second of three straight on the road at Miami on Wednesday. The Eagles travel to face top-ranked and unbeaten Syracuse, also on Wednesday.
The Irish had two starters from Massachusetts (Connaughton and Auguste). Both received a nice hand.