Mark Scheifele also scored for Winnipeg (26-14-3), which earned its fourth win in five games and avenged a 4-2 loss to Ottawa on Monday night.
''I think it starts with leadership, those guys get everyone going,'' Lewis said. ''We have a tight group in there, we know how to win.
''We know we just had to stick with it there and came out and had a good third.''
Laurent Brossoit was in goal for Winnipeg after Connor Hellebuyck had made seven straight starts. Brossoit finished with 27 saves.
The Jets moved to within five points of North Division-leading Toronto (28-11-4), which was idle.
Josh Norris and Nick Paul scored for Ottawa (14-26-4), which fell to 9-10-4 at home this season. Matt Murray finished with 32 saves.
After a scoreless second period, Perreault put Winnipeg ahead 2-1 at 2:07 of the third. Perreault fired a high shot past Murray on a power play for his ninth goal of the season.
Lewis scored short-handed at 9:39 to put Winnipeg ahead 3-1. It was Lewis' third of the year.
''It was a tight game throughout the whole thing,'' Lewis said. ''We knew they were going to come hard and we needed to keep it simple.
''In the third, we got a big power-play goal from (Perreault), that was an awesome shot. Obviously, with the short-handed goal it was a big win for us.''
Norris scored a power-play goal with 10 seconds left to pull Ottawa to within 3-2. Norris has 12 goals this season.
Murray was making his first start in goal for Ottawa since March 10. He suffered an upper-body injury in warmups before a game against the Toronto Maple Leafs on March 14.
''I felt pretty good all things considered,'' Murray said. ''It has been quite some time so (my) timing felt a little bit off.
''Traffic is hard to duplicate in practice. In a game, there's just so many layers. That's always the biggest adjustment when you haven't played in a while. They did a good job of getting traffic to the net but all things considered I felt pretty good.''
Ottawa went 5-6-3 without Murray, using four goalies -- Joey Daccord, Filip Gustavsson, Anton Forsberg and Marcus Hogberg -- in his absence.
Ottawa's Connor Brown had his club-record goal-scoring streak halted at eight games. He was looking to become the first player since Teemu Selanne in 1997-98 to score in nine straight.
Ottawa opened the scoring with Paul's fourth goal of the season just 1:19 in. But Scheifele countered at 3:24, converting Nikolaj Ehlers' backhand pass for his 16th of the year as Winnipeg outshot the Senators 11-9.
Jets: At Toronto on Thursday night to wrap up a five-game trip.
Senators: At Montreal on Saturday to open a four-game trip.
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