Trevor Zegras scored, and John Gibson made 35 saves for the Ducks (12-25-4), who were looking to win three in a row for the first time this season.
The Bruins were playing the second of a back to back following a 4-2 win at the San Jose Sharks on Saturday night.
"You can learn from them, really," Anaheim forward Adam Henrique said of Boston. "The way they play, a veteran team in a tough back to back that seemed like a home game for them. There's still lots to learn here."
Pastrnak gave the Bruins a 3-1 lead at 11:56 of the second period, scoring with a wrist shot from the right circle on a power play. He then scored 17 seconds later on a breakaway to extend the lead to 4-1.
"Through two periods, it's 4-1 and we made maybe five mistakes and three of them ended up in our net," Ducks coach Dallas Eakins said. "We can't make those mistakes."
Brad Marchand pushed it to 5-1 at 6:20 of the third period when he recovered a puck behind Anaheim's net and scored on a wraparound.
Hampus Lindholm, who was playing his first game in Anaheim since being traded to the Bruins on March 19, scored from the bottom of the left circle to make it 6-1 at 11:26.
"It was a different feeling, but happy with the two points and the process," Lindholm said. "We were playing good on this road trip here, so it's nice to go back home with a big win."