Riemsdyk scored for the first time in 15 games at 6:38 in the first period, on a power play. Niklas Kronwall was in the box for high sticking.
Alexey Marchenko and Nazem Kadri also sounded the siren for the Leafs, who had a record of 0-2-3 in their last five games.
Mitch Marner and Tyler Bozak received two assists each.
Gustav Nyquist scored twice for Detroit. Henry Zetterberg was an accomplice to each goal, scoring at least one point in a seventh straight game.
Goalkeeper Frederik Andersen made 22 saves, three fewer than Petr Mrazek. This was his eighth consecutive start.
The Red Wings have lost their last three games, always with one goal.