Pastrnak, who was playing his 100th NHL game, had at least a point in each of Boston's three games. He's tied for the NHL lead with four goals (Auston Matthews of Toronto Maple Leafs, Richard Panik of Chicago Blackhawks) and has two assists.
Bruins forward Dominic Moore scored 19 seconds after Blake Wheeler had given the Jets a 1-0 lead midway through the first period.
Boston defenseman Brandon Carlo scored his first NHL goal in his third game to make it 3-1 with 1:59 remaining in the third period, and Zdeno Chara scored an empty-net goal with 49.1 seconds left.
With an assist on Pastrnak's goal, Brad Marchand had at least a point in each of the Bruins' three games and leads the NHL with seven points (two goals, five assists).
Wheeler scored a goal in each of Winnipeg's first three games, but the Jets have lost two in a row since a season-opening 5-4 overtime win against the Carolina Hurricanes.
The Bruins thought they had taken the lead earlier in the second period.
After Chara's wrist shot from the point deflected off the stick of Winnipeg defenseman Ben Chiarot and eluded goalie Connor Hellebuyck at 4:43 of the period, coach Paul Maurice challenged that the play was offside. Video review showed Boston's Ryan Spooner entered the zone before the puck, nullifying the goal.
Bruins goalie Tuukka Rask made 34 saves, including 13 against the Jets power play. The Boston penalty kill was 5-for-5, all in the first 28 minutes.
"[Rask] was absolutely the best player on the ice," Pastrnak said. "When the score was 1-1, they had big chances, and he kept us alive. He and the PK did a [great] job today, big credit to them."