Rasmus Sandin scored for the Maple Leafs (26-10-7), who played without Auston Matthews (undisclosed injury) for the second straight game. Ilya Samsonov made 19 saves.
Toronto won 2-1 against the Nashville Predators on Wednesday.
"Auston is one of the best players in the world, if not the best, so we're obviously better when he's in the lineup," Sandin said. "We worked hard tonight to try to make up for it, but he's got big shoes to fill. If he's out there tonight, he probably puts in a puck if not two, three or four."
Bobby McMann appeared to give the Maple Leafs a 1-0 lead 56 seconds into the first period when he tried to kick the puck onto his stick, but it deflected in off Olli Maatta's skate. After video review initiated by the NHL Situation Room, the goal was disallowed because McMann had kicked it and it had gone in without hitting another stick.
McMann was playing his second NHL game.
"That was sad, because it is his first NHL goal, he's celebrating and we're all really happy for him," Samsonov said. "We weren't sure what was going on, and then it was no goal."
Raymond made it 1-0 at 8:48, beating Samsonov off a drop pass from Dylan Larkin.
Robby Fabbri scored a power-play goal at 3:49 of the second period, putting Detroit ahead 2-0. Fabbri, who returned Jan. 4 after missing 10 months with a knee injury, has scored in three straight games.
"Goals are great, so I'm not going to complain about that, but I'm just trying to get my game back into shape," he said. "Toronto has had our number for a while, so it feels good to get a win."