The win was Winnipeg's third in a row following a nine-game winless streak.
Cole Perfetti, Morgan Barron and Brayden Yager also scored for the Jets.
Stuart Skinner made 17 saves for Winnipeg, who moved to 7-8-3.
Erik Cernak had a pair of assists for the Lightning.
Andrei Vasilevskiy turned aside 22 shots for Tampa Bay, who dropped to 10-4-2 on the season.
There was no scoring in the first period.
Cole Perfetti opened the scoring 1:53 into the second on the power play when he moved into the slot before Mark Scheifele slid him the puck and he made no mistake, wiring a wrister past Tampa goaltender Andrei Vasilevskiy beating him glove side to put the Jets up 1-0.
The goal was his 7th of the season.
Morgan Barron scored 12:38 into the second after Neal Pionk took control of the puck deep in the Tampa Bay zone and circled the net before finding Barron and hitting him with a cross slot feed which the Jet forward one timed past Vasilevskiy to make it 2-0 Jets.
With Pontus Holmberg serving a double minor for high sticking Braden Yager, the Jet rookie made him pay, scoring his first NHL career goal after Viggo Bjorck relayed an Alex Iafallo feed through his legs to a wide open Brandon Hagel got the Lightning on the board at 10:22 when he beat Skinner high from in tight after Anthony Cerelli stripped Braden Yager of the puck behind the Winnipeg net before feeding Hagel who cut in front of the net and scored.
The goal was his 9th of the season.
Pontus Holmberg pulled the Lightning to within one with just under six minutes remaining in regulation when he buried a rebound off an Erik Cernak point shot to make it 3-2.
Holmberg scored again 26 seconds later to tie the contest at 3 when Erik Cernak slid him the disc as he crossed in front of the net which the Lightning forward simply slid past Skinner to make it 3-3.
The goal was his 6th of the season.
Scheifele then scored his game winning power play goal with .3 seconds remaining to seal the win for the Jets.
SHOTS-TAMPA BAY 20 WINNIPEG 25
ATTENDANCE-14,307
