Detroit was 3-for-3 on the penalty kill after going 3-for-3 on Saturday.
Hedman scored to make it 4-1 at 4:12 of the third period on a wrist shot from above the circles.
It ended a goal drought of 96:46 for the Lightning, who had not scored since 7:26 of the first period in a 2-1 win against the Red Wings on Saturday. Tampa Bay's 129 goals (3.39 per game) are tied for third in the NHL with the Florida Panthers (3.31), behind the Colorado Avalanche (132; 3.57) and Washington Capitals (130; 3.42).
"Everybody likes to score, and when you're used to scoring and you don't, it gets a little uncomfortable," Lightning coach Jon Cooper said. "Then you start taking shortcuts thinking you can give yourself a better opportunity to score. The only way you can do it is to work your way out of it.
"Eventually pucks that might not go in will start going in. It's the cycle of hockey and we just have to work our way through this."
Darren Helm scored an empty-net goal at 14:19 to make it 5-1.
"[The win is] huge, everyone knows they won a Stanley Cup and they are one of the top teams in the League," Greiss said. "It's always special to beat those kinds of guys."
NOTES: Lightning goalie Curtis McElhinney "tweaked something" Saturday and was unavailable to play, Cooper said, leading to Gibson getting the start. … Tampa Bay defenseman Ben Thomas had one shot on goal and was minus-1 in 14:23 in his NHL debut. … Glendening and Anthony Mantha each had two assists for the Red Wings. … Filppula's goal was his first since Feb. 19 against the Florida Panthers. He did not play in 14 straight games from March 2-April 1. . … Stamkos had an assist but has not scored a goal in the past six games, his longest drought of the season.