The Red Wings (0-2-2) hadn't lost the first four games of a season since going 0-5-0 in 1980-81.
"I think we learned we need to compete for 60 minutes if we want to win games," Red Wings coach Jeff Blashill said. "When we play hard we can make some good things happen, but we have to do that for 60 minutes."
Nick Jensen, who hadn't scored in 87 games, had two goals for Detroit, and Jimmy Howard made 30 saves.
"It's exciting any time you can contribute offensively to the team," said Jensen, who had his first multigoal NHL game. "It isn't as sweet when you get the goals and don't get the win, though."
The Red Wings took a 1-0 lead at 7:18 of the first period when Jensen scored to finish a 3-on-1 break.
Rielly tied it 1-1 at 15:48, one-timing a Marner pass inside the far post.
"Morgan is playing great hockey right now," Marner said. "He's running things on the power play and making chances for everyone, but he also knows when to jump into the rush at even strength."
The Maple Leafs scored twice in the second period and outshot the Red Wings 15-5.