Nino Niederreiter, Morgan Barron and Nate Schmidt scored for the Jets (38-26-3), who were playing the second of a back to back following a 5-4 overtime victory against the Florida Panthers on Saturday.
"It's huge. … Two tough barns, especially the last couple of years with how good Florida is," Winnipeg associate coach Scott Arniel said. "It's a real desperate time for us. We have to keep pace with everyone in our Division (Central) and Conference (Western). We knew it was going to be a tough (three-game) trip, and it's off to a great start."
The Jets moved one point ahead of the Colorado Avalanche, who have three games in hand, for third place in the Central.
"We know all the points matter right now, and our schedule doesn't get easier," Barron said. "And the next two games are against really good teams with [the Carolina Hurricanes] and Boston (Bruins) coming up."
Anthony Cirelli had a goal and an assist, Brandon Hagel had two assists, and Andrei Vasilevskiy made 19 saves for the Lightning (39-22-6), who were also playing the second of a back to back following a 3-1 win against the Chicago Blackhawks on Saturday.
Tampa Bay, which finished a four-game homestand 2-1-1, remained four points behind the Toronto Maple Leafs, who have two games in hand, for second in the Atlantic Division.
"Are we a better team now than we were? No question," Lightning coach Jon Cooper said. "Is it disappointing to only get five of eight points? It is. We definitely thought we should have gotten points out of this game, and we didn't. And we thought we should have gotten two points against Vegas (a 4-3 overtime loss to the Golden Knights on Thursday). Now we've just got to go on the road and get some on the road."