It was Pittsburgh's (10-5-0) seventh road win of the season, while Winnipeg (5-7-1) has now lost three straight at home and hosts Boston on Sunday.
After a couple swipes at rebounds, Adams recorded his first goal of the season at 3:19 of the first period. His second was into an empty net in the final minute of regulation.
The Pens have now scored first in an NHL-best 12 games this season, including all nine on the road. They’re now 9-3 when scoring first.
Defenceman Kris Letang assisted on Adams' goal, giving him six points in his last six games, including two goals.
The Jets took a hit to their lineup before the midway point of the first period when leading scorer Tobias Enstrom left the game holding his right arm. Entering the game, the defenceman had two goals and 13 points.
Winnipeg did have defenceman Zach Bogosian back for his first game of the season after recovering from wrist surgery. He ended up logging just under 26 minutes of ice time.
Pittsburgh outshot the Jets 12-6 in the opening period, with Winnipeg only recording its third shot around the 17-minute mark.
The Jets turned the tables in the second, outshooting the Pens 14-9 but with nothing in goal to show for the offensive outburst.
Neal's third-period goal came after the Jets took two penalties 24 seconds apart. Zach Redmond was called for interference at 13:18 before fellow defenceman Mark Stuart was sent to the box for tripping.
Notes: Penguins defenceman Brooks Orpik, who assisted on Adams' second goal, was playing in his 600th NHL game. ... Winnipeg forward Eric Tangradi made his debut with the Jets. He was traded from Pittsburgh on Wednesday for a seventh-round pick in this summer's draft.