New Jersey also got goals from Dawson Mercer, Jimmy Vesey and Tomas Tatar.
Jan Rutta, Pat Maroon and Victor Hedman scored for the Lightning, who had a nine-game point streak end. Andrei Vasilevskiy made 22 saves.
Sharangovich, who also had an assist, got the Devils’ third straight goal to start the third from the low left circle to put New Jersey up 4-3 at 9:34. Tatar had an empty-net goal.
Rutta opened the scoring 5:49 into the game, but Sharangovich tied it with six minutes left in the first when the center stopped a 16-game goal drought. Then Maroon put the Lightning up 2-1 during Tampa Bay’s third power play with 1:45 left in the first.
Tampa Bay took a 3-1 lead at 6:17 of the second when Hedman skated in alone from the blue line and scored from the left circle off a pass from Boris Katchouk.
Mercer got the Devils within 3-2 with a nifty goal 1:12 into the third. He started to skate around the net but reached back with his stick and stuffed the puck past Vasilevskiy.
Shortly after Blackwood made a terrific glove save on Alex Killorn during a two-man breakaway, Vesey made it 3-3 on a breakaway at 5:39.
The Devils are an NHL-worst 1 for 22 on road power plays after failing to score on three chances. New Jersey allowed a breakaway and 3-on-1 during a second-period power play.
Lightning RW Corey Perry, who had a first-period shot from the low left circle stopped, has not scored a goal in his last 36 games. He has one assist in 16 games this season and was given a minor penalty in the second for an illegal check to the head on Devils C Nico Hischier, who was OK after the hit.
Devils: Host Minnesota on Wednesday night.
Lightning: Complete back-to-back home games with a contest Sunday against Minnesota.