Jack Campbell made 20 saves for his fifth shutout of the season and William Nylander had two assists for the Maple Leafs (53-21-7), who are 6-1-1 in their past eight games.
"That (home ice advantage), I'm excited about," Toronto coach Sheldon Keefe said. "To start the playoffs and have fans on our side, you could see it tonight just how excited they are for our team. No matter who it is, it's going to be an absolute battle and we're going to need that edge. To start that way, it gives us an opportunity to play in front of our fans, we were in control of the situation and we took care of it today. I'm happy for our guys that way. We have one game left to play but obviously we are very much focused on what's coming, whoever it is."
Alex Nedeljkovic made 33 saves for the Red Wings (31-40-10), who are eliminated from playoff contention.
"They had looks earlier in the game but I thought we did a pretty good job of keeping them to the outside," Red Wings forward Sam Gagner said. "'Ned' played great, gave us a chance. That's certainly a tough one to give up."
"If you scored 60, you're finding ways to get it done no matter who you are matching up against. [Matthews is] a really special talent, one of the top players in the League, certainly probably the top goal-scorer. He's going to get his looks and you just try to limit him and keep him to the outside as much as you can. Ultimately he found a way to break through tonight."
Matthews put the Maple Leafs up 1-0 at 15:48 of the second period when he took a pass from Jason Spezza in the slot and backhanded a shot past Nedeljkovic's outstretched glove. The goal ended a five-game drought, which was his longest of the season.
"We put ourselves in position going into the third period to win a hockey game," Red Wings coach Jeff Blashill said. "We would have preferred it to be 0-0, we would have preferred for us to have the lead but it's 1-0 and certainly the game is there to be had. We just weren't able to make the play to score the next goal and unfortunately they got it."