Detroit had a 3-0 lead midway through the game, but allowed the Blues to come all the way back to tie it.
Jimmy Howard, back in net for the Red Wings after missing two games with a bruised right knee, had 26 saves in the win and didn’t face a shot in overtime.
Patrick Eaves, Todd Bertuzzi and Jakub Kindl also scored for the Central Division-leading Red Wings, who won for the second time in three games.
T.J. Oshie, Patrik Berglund and David Backes scored goals to tie the game, but the Blues lost for the seventh time in nine games.
Jaroslav Halak kept them from losing in regulation, making a spectacular sliding save with his left pad in the final minute. But he was unable to stop Helm’s one-timer from the slot on a centering pass from Jiri Hudler.
Halak finished the game with 25 saves.