Todd Bertuzzi also scored for Detroit, which had three power-play goals to snap its 0-for-10 season-opening man-advantage skid. Daniel Alfredsson had three assists and Jimmy Howard made 32 saves.
Erik Gustafsson and Tye McGinn scored for Philadelphia and Ray Emery stopped 25 shots. Flyers interim coach Craig Berube dropped to 1-2 since replacing the fired Peter Laviolette on Monday.
Kronwall's power-play goal with 8:52 left in the second period gave Detroit a 2-0 lead. Kronwall's first goal of the season came on a wrist shot from the left circle.
Gustafsson put Philadelphia on the board just 34 seconds later when his floating wrist shot from the right point found its way into the net.
Datsyuk restored the two-goal lead with his power-play goal 3:08 into the third period, beating Emery with a backhand shot from the slot that was screened by Bertuzzi.
McGinn made it 3-2 with his first NHL goal, 2:38 later. He backhanded a rebound in from the slot after being called up from the minors earlier in the day.
Zetterberg scored with 6:12 remaining and added an empty-netter in the final minute.
Bertuzzi opened the scoring, with the Red Wings' first power-play goal of the season, 7:13 into the game. He put a wrap-around effort past Emery for Bertuzzi's first goal, just 24 seconds after Michael Raffl went off for hooking.
