Howard has two shutouts in a week and three for the season. He's tied for the NHL lead with Nashville's Pekka Rinne and Jonathan Quick of the Los Angeles Kings.
"He's been our best player so far this year, together with Nick (Lidstrom)," said defenseman Niklas Kronwall, who scored Detroit's second goal.
The Wings became the first team this season to score more than twice against Edmonton's Nikolai Khabibulin, who came into the game with a 7-0-2 record and an NHL-low 0.98 goals-against average. Khabibulin was often superb in stopping 27 of 30 shots, but got no offensive support as the Oilers lost for the second time in as many nights and fell to 2-3-0 on their six-game road trip.
Though the Wings scored just three times, they had much the better of play.
"There more you play in their zone, the more fun it is anyway," coach Mike Babcock said.
Edmonton has lost three of four after winning six in a row and was shut out for the first time this season.
"We want to get our game going the right way," Oilers forward Taylor Hall said. "It's simple hockey but the last few games haven't been that."
Detroit has won three straight after a six-game losing streak.
Drew Miller opened the scoring 10:35 into the game, beating Khabibulin with a quick shot after the puck caromed off two Oilers for his first of the season.
Kronwall's slap shot from the blue line 2:05 into the second beat Khabibulin high to the blocker side to put Detroit ahead 2-0.
"We just tried to fire as many pucks as possible on the goaltender," Kronwall said.
"We had small successes along the way, but that's a good team that took advantage," Oilers coach Tom Renney said. "Our battle level weaned as time went on."
The Oilers will try to avert their first three-game losing streak this season when they visit Chicago on Sunday. Khabibulin knows they can't give the Hawks the same kind of chances they allowed to the Red Wings.
"Everything's correctable if you want to correct it," Khabibulin said. "We're still learning, we're still a young team. We're going to make mistakes."
Material from team media was used in this report