Zetterberg scored 1:23 into overtime, lifting Detroit to a 3-2 win over the Phoenix Coyotes on Monday night.
It was the Red Wings' first game at home after a three-game road trip. They traveled all day Sunday after dropping a 6-4 decision in Vancouver on Saturday night.
"We know this game is a tough one, both in the legs and mentally," Zetterberg said. "We knew it was not going to be a beautiful win if we were going to get the W. It was a pretty ugly one. We're taking it and happy to get the day off tomorrow."
The Coyotes' Scottie Upshall beat Howard with a slap shot from the left circle but hit the crossbar with 2:50 left in regulation.
"We worked hard, had our chances. Both goalies played well," Phoenix defenseman Ed Jovanovski said. "Sometimes those are the toughest."
Zetterberg tipped in Ruslan Salei's shot from the top of the left circle as a penalty was being called on the Coyotes. Howard raced to the bench as Detroit maintained possession of the puck and Todd Bertuzzi jumped off the bench to replace Howard to give the Red Wings a 5-on-4 advantage.
Bertuzzi took a pass from Zetterberg just after Bertuzzi raced over the blue line along the right wing boards. Bertuzzi then made a cross-ice pass to Salei. He moved in to the top of the left circle and aimed a shot at Zetterberg's stick. The puck hit the target and trickled through Bryzgalov's pads and into the net.
It was Zetterberg's fourth goal.
"Bert made a good pass to Rusty and he really held onto the puck, so I had a chance to get to the side of the net," Zetterberg said. "He made a good shot pass, I just put the stick there and it went in."
Phoenix is 0-5 in overtime this season.
"That can't happen. And it's not like they're making the great play to beat us," Coyotes coach Dave Tippett said. "We're making the mistake to give them the game."
Lidstrom's second goal of the season tied the game at 2, 7:24 into the third period on a slap shot from the left point.
"Down that goal going into the third, it was good to battle back," Detroit defenseman Brian Rafalski said.
Yandle gave the Coyotes a 2-1 lead 7:31 into the second period when he picked up a loose puck in the lower left circle off the rush and beat Howard. It was Yandle's third goal.
Cleary opened the scoring 1:40 into the game when he put in the carom off the end boards of Rafalski's wide shot into an empty net. It was Cleary's fourth goal and third in three games.
Hanzal took advantage of a favorable bounce at the other end to tie the game with 55 seconds left in the opening period. Derek Morris' shot from the point went wide but came off the end boards between Howard and the goal post and Hanzal poked it into the net. It was Hanzal's second goal, both against Detroit.
Howard was down in his crease for about a minute with 6:04 left in the first period. Phoenix right wing Lee Stempniak knocked Salei into Howard, who remained in the game after being attended to by Detroit trainer Piet Van Zant. Stempniak received a 2-minute interference minor. Stempniak also got a goaltender interference penalty in the second period when he bowled over Howard.
- Rafalski returned after missing 10 games because of arthroscopic knee surgery.
- Cleary's goal extended his point streak to five games (3-4-7).
- Coyotes' C Vernon Fidler limped off the ice and went to the dressing room after being tripped by Niklas Kronwall 9:41 into the second period. Fidler later returned.
- Red Wings' owner Mike Ilitch told the Detroit Free Press, in an on-line story, that he was close to buying the NBA's Detroit Pistons. Ilitch, who also owns major league baseball's Detroit Tigers, has been negotiating with current Pistons' owner Karen Davidson. Ilitch was in Toronto watching Detroit senior vice president Jimmy Devellano and former Red Wing Dino Ciccarelli being inducted into the Hockey Hall of Fame.
- Lidstrom's goal ran his point streak to nine games (2-10-12).
- Pavel Datsyuk had an assist on Lidstrom's goal to stretch his point streak to nine games (4-8-12).