"That was as close to a 60-minute game as we’ve played," Lightning coach Jon Cooper said. "I think we dictated the play most of the game.
"Give Detroit credit. We bent but we didn’t break."
Howard had 27 saves.
Detroit trailed 3-2 at the end of the second period thanks to Darren Helm’s slap shot goal and Gustav Nyquist tied the game midway through the third with his team-best eighth tally.
Stamkos’ second goal, his 10th this season, ricocheted in off the right post early in the second period to give the Lightning its first lead and Tyler Johnson made it a 3-1 game a few minutes later.
Detroit’s Johan Franzen opened the scoring six minutes in on the first shot of the game’s first power play when he knocked home a centering pass from Niklas Kronwall. Tampa Bay answered later in the period when Stamkos scored during a 5-on-3 power play.
The Red Wings had three good scoring chances during sudden death, including Kronwall’s point-blank shot that missed the mark.
"I knew there was going to be a pass so I got over there pretty quick and he went high," Bishop said.
The biggest save came from Howard, who made a pad save on Jonathan Drouin’s wraparound shot with less than 20 seconds left.
Detroit was happy to come away with a point but fell to 0-3 in shootouts a season after going 5-9 in them.
"We haven’t been good enough. We can’t seem to find a way to score; then we don’t win shootouts," Nyquist said. "It’s tough. We want to get that extra point when it comes down to it but we haven’t been able to do it this year."
His coach won’t be losing any sleep over his team’s shootout struggles.
"Right now it isn’t working the way we want but we should’ve shot it into the net in overtime when we had all those chances, so I’m going to spend no time worrying about it, " Detroit’s Mike Babcock said.
The Lightning, which had scored at least four regulation goals in each of its first five wins during the streak, will be in Chicago on Tuesday to complete a three-game road trip.
Notes: Detroit center Pavel Datsyuk missed his second straight game with a sore groin. … Tampa Bay was without defenseman Victor Hedman (fractured finger), center Alex Killorn (upper body) and winger Brett Connolly (lower body). … Red Wings defenseman Kyle Quincey started Sunday evening after missing three games with an ankle injury.