Kyle Connor had a goal and an assist.
Josh Morrissey had three assists for the Jets Connor Hellebuyck made 26 saves for Winnipeg, who moved to 25-13-1 and within a point of the Central Division leading Dallas Stars with one game in hand.
Anthony Cirelli had a goal and an assist for the Lightning Andrei Vasilevskiy stopped 16 shots for Tampa Bay, who dropped to 24-13-1.
Anthony Cirelli got the Lightning on the board 11:48 into the first period when he banged home a rebound off a Steven Stamkos shot to make it 1-0.
The goal was his 2nd of the season.
Pierre-Luc Dubois tied the game in the last minute of the first when he got his stick on Kyle Connor's shot from the left circle.
Connor skated in, paused and wired a wrister which Dubois tipped past Vasilevskiy to make it 1-1 at 19:21.
Nikita Kucherov gave Tampa Bay the lead 1:35 into the second when he converted a Ian Cole feed wiring a forty foot wrister past Hellebuyck to make it 2-1.
The goal was his 14th of the season.
Dubois netted his second of the night on the power play just over seven minutes into the second period when he got his stick on a Josh Morrissey shot from the high slot and deflected the puck past Vasilevskiy to knot the contest at 7:05.
The goal was his 19th of the season.
Kyle Connor fired a power play marker 5:38 into the third period to give the Jets their first lead of the night.
With Winnipeg enjoying a two-man advantage, Mark Scheifele hit Connor with a crisp, cross-ice feed which he one timed past Vasilevskiy, beating him with a low shot.
The goal was his 17th of the season.
Morgan Barron scored on a shorthanded wraparound to make it 4-2 and seal the win for the Jets.
The goal was his 4th of the season.
Winnipeg hosts Vancouver Sunday while Tampa Bay returns home to face Columbus Tuesday.
SHOTS-TAMPA BAY 28 WINNIPEG 20