Maple Leafs goalie Dennis Hildeby lunged out of his net to push a loose puck toward Auston Matthews in a clearing attempt, but Edvinsson got to it first at the blue line, skated to the net and slid the puck inside the right post with a backhand.
The Red Wings (23-14-3) have won four of five. Cam Talbot made 25 saves.
John Tavares had two assists for Toronto (17-15-6), which has points in three straight games (2-0-1). Hildeby made 33 saves.
Detroit forward Patrick Kane returned to the lineup after missing six games with an upper-body injury. He is two goals short of 500 in his NHL career.
Toronto used some quick passing on the power play to take a 1-0 lead at 4:25 of the second period. Tavares found Matthews in front of the net and he flicked the puck to Matthew Knies, who beat Talbot while falling to the ice.
Moritz Seider tied the game at 19:01, scoring his seventh goal with a shot through traffic after Lucas Raymond hit the post.
Nicholas Robertson put the Maple Leafs up 2-1 at 4:53 of the third period, scoring with a slap shot from the top of the face-off circle after Tavares forced a turnover along the boards.
Mason Appleton, though, tied the game 23 seconds later, getting a step to the outside of Troy Stecher and beating Hildeby over his glove.
The Red Wings nearly won the game in the final 90 seconds, but Hildeby made a sprawling pad save on Andrew Copp and his attempt on the rebound hit the post.
