"We have some guys out and I knew I had to step up," said Datsyuk, who also had two assists.
Datysuk broke down the right wing with Valtteri Flippula coming down the slot, stopped at the right face-off circle and ripped a slap shot at 15:54 for his 15th of the season. Kris Draper added an empty-net goal at 19:25.
The win was Detroit's fourth in a row and their sixth in seven games.
"[Datsyuk] is playing at another level," said Wings coach Mike Babcock. "He usually plays against the opposition's best line, and right now, "he's outplaying them."
Datsyuk's goal was his 15th and behind Zetterberg's 25, and Holmstrom's 17 goals as team leaders.
"Pavel really stepped up when we needed him," said captain Nicklas Lidstrom. "He has that ability to just pull up and make things happen. He knows how to keep control and get the shot off."
In the first period, Mikael Samuelsson converted a centering pass from Jiri Hudler inside the right post and into his sixth goal of the season at 15:12.
With two goals 25 seconds apart in the second period, Phoenix gained the lead.
"We're playing a tight game with one of the best teams in the league," said Vrbata. "Our power play cost us the second game in a row because we did not score when we should."
The Coyotes' inability to score with the man advantage continues to baffle coach Wayne Gretzky. Phoenix went 0-4 on the power play.
"We talked about the power play for the last four days," Gretzky said. "Our power play has to score and contribute."
The Wings tied the game with a four-on-three advantage. Brian Rafalski's slap shot from the circle beat Ilya Bryzgalov at 18:25 of the second.
Vrbata's penalty shot was the first for Phoenix since Shane Doan was unsuccessful March 18 against Dallas' Marty Turco ... Jovanovski's goal was the 100th of his NHL career, and 14th in a Phoenix uniform ... Samuelsson scored in his second straight game, and third in his last five games ... With a first period assist, the Wings' Nicklas Lidstrom has at least one point in seven of his last eight games ... Wings' leading scorers Henrik Zetterberg and Tomas Holmstrom each missed their fourth straight game.