The Red Wings were outshot 14-4 in the first period, when they fell behind 1-0. For the rest of the game, they outshot the Sharks 31-8.
"I thought we just kept playing," Red Wings coach Mike Babcock said. "Obviously we weren't very impressed with our first, but we're a good skating team and we know how to play and we're competitive. If you compete at a high level, you have a chance. That's what the game's all about. The game's fair every night.
"If you compete hard, you get rewarded, and if you don't, you're not rewarded. I like that the guys found a way to win."
Luke Glendening scored the game-winning goal with 1:15 left. Gustav Nyquist tracked down a loose puck behind the net and sent it in front to Glendening, who put a backhand shot from close range past Sharks goalie Antti Niemi.
"Just resiliency," Howard said of the Red Wings' comeback win. "I don't think we ever feel we're ever out of a game. We just keep playing until the final buzzer. It's great to see, especially from a young team. I think a lot of guys are maturing throughout the year here, and it's going to be great for down the stretch and in the playoffs."
Matt Irwin and Patrick Marleau scored, and Niemi made 31 saves for San Jose (30-24-8), which suffered another blow to its playoff hopes. The Sharks trail the Minnesota Wild by three points for the second wild-card spot in the Western Conference for the Stanley Cup Playoffs
"We were happy with our first (period), but the tables turned," Irwin said. "They picked their game up, and we didn't elevate our game. We were well aware they were going to play better in the second period. We didn't push back.
"It's devastating. This time of the year, it's unacceptable. This is where we have to put points in the bank and set ourselves up for the stretch run. And to not get these points is extremely frustrating."
The Sharks had a 2-1 lead to start the third period, but the Red Wings had the momentum after a strong second.
Then at 7:33 of the period, Sharks forward Matt Nieto was given a four-minute penalty for high sticking Tomas Jurco. San Jose killed off the double-minor against Detroit, which has NHL's No. 1 power play.
"He's a special player," Howard said of Datsyuk. "He's one of the best in the world. Just thankful that he's on our side every night."
The Sharks hadn't played since Saturday, when they lost 2-1 to the Los Angeles Kings in the 2015 Coors Light NHL Stadium Series game at Levi's Stadium, and they came out in the first period with plenty of energy.
San Jose took a 1-0 lead on Irwin's sixth goal at 7:06. Irwin sent a shot from the blue line through heavy traffic that beat Howard to his glove side.
The Sharks had chances to add to their lead in the first period, including two power plays, but Howard stopped the final eight shots he faced.
The Red Wings didn't have a shot on goal until Glendening tested Niemi at 8:23 of the first period.
"We were talking before the game that the first 10 minutes is going to be critical, they're coming hard for sure, like they did, and we weren't ready for it," Pulkkinen said. "I don't know why because we knew that they were coming hard. But as the game went on, we were playing really good, and I think we deserve to get the two points.
"We have a great group of hardworking guys. When we keep working like that, it's going to be good. We knew even when we were losing 2-1 after 40 (minutes) that we can get a goal or two and we found a way to get two goals."
Detroit outshot San Jose 18-6 in the second period, when each team scored a goal.
After Sharks defenseman Brent Burns went to the penalty box for hooking Datsyuk at 3:10, Pulkkinen scored on the power play.
Early in the power play, Stephen Weiss fired a shot that broke defenseman Marc-Edouard Vlasic's stick, putting San Jose into a deeper bind. Weiss sent the puck toward the net, and it bounced off Vlasic's skate to Riley Sheahan, who passed it to Pulkkinen in the left circle, and the rookie forward beat Niemi for his second NHL goal.
"It was a great play for the guys," Pulkkinen said. "I was wide open backdoor, so it was kind of an easy goal for me to put it in."
The Sharks answered on the power play when Marleau scored his 450th career goal at 6:51.
With Jonathan Ericsson in the penalty box for interference, the Sharks needed nine seconds to score while up a man. Logan Couture's shot was deflected wide to the right of the net, and the puck went off the back boards and bounced back toward the crease. Joe Pavelski poked the puck ahead to Marleau, who elevated a shot from close range past Howard.
The Red Wings turned up the heat on Niemi for the remainder of the period, but they couldn't get the puck past him again.
With 1:28 left in the second period, Pulkkinen fired a shot that bounced off Niemi, landed behind him in the blue paint and trickled toward the net. A diving Niemi got his stick on the puck and stopped it from going over the goal line.
In the closing seconds, Niemi made back-to-back saves of Tatar shots, first with his left pad, then with his glove.
But in the third period, the Red Wings broke through to score twice against San Jose, which had gone 12-2-1 in its previous 15 games against Detroit.
"We were back on our heels and took too many penalties in the third," Couture said. "They skated better than we did. They got pucks deep. We didn't. They skated the puck good through the neutral zone. We need to find ways to win games. We're finding ways to lose games right now."
Red Wings defenseman Brendan Smith left the game with 3:57 remaining after sustaining an apparent hand injury. Babcock had no update on his condition.
Detroit captain Henrik Zetterberg missed his third straight game since being punched in the head by the Dallas Stars' Jamie Benn on Saturday. Red Wings defenseman Kyle Quincey missed his fourth straight games with bone chips in his ankle.