The goal was Gudas' first as a Duck.
Vaakanainen's assist marked his first point of the year, and the first of his career against his original NHL team. With the secondary assist, Strome has points in three straight games (1-2=3).
Boston tied the game early in the second on a good break of their own, as Pastrnak's misfired one-timer when right to Coyle for a tap-in on the backdoor.
Pastrnak has 18 points in 16 career matchups against Anaheim.
Grezlyck put Boston in front 80 seconds later, getting just enough of his one-timer from the left circle to sneak it through Gibson's five-hole.
Pastrnak capped Boston's three goal-middle frame by converting his own rebound in the slot after a shot on left wing.
McAvoy assisted on all three Boston goals and is now tied for second among NHL defensemen in helpers (six) this season.
And just when it seemed like Anaheim would fall short despite a flurry of late chances, the Ducks stunned the Boston crowd with a pair of goals in the final two minutes of regulation to force overtime, all while Gibson was pulled for the extra attacker.
Carlsson pulled the Ducks within one, crashing the net and calmly tapping home the rebound after close calls by Trevor Zegras and Troy Terry in tight.