Harley scored on a wrist shot from the point after Wyatt Johnston won a face-off back to him out of the right circle.
Matt Duchene scored twice, Harley had a goal and an assist, and Jason Robertson had two assists for the Stars (30-14-9), who ended a three-game road losing streak in which they scored two goals. Jake Oettinger made 23 saves.
Brayden Schenn scored two goals, and Jimmy Snuggerud had two assists for the Blues (19-25-9), who lost their fifth straight (0-4-1). Jordan Binnington made 20 saves.
St. Louis tied the game with three straight goals in the third.
Robby Fabbri cut it to 3-1 at 3:15 on a wrist shot from the slot.
Schenn then made it 3-2 on the rush at 6:22, scoring with a wrist shot from the left circle to the far side off a cross-ice feed from Snuggerud.
Schenn tied it 3-3 at 15:50. Harley's clearing attempt around the boards hit one of the officials in the right corner before Snuggerud got to the loose puck and passed to Schenn in the left circle for a wrist shot that went under the bar.
Duchene made it 1-0 on the power play at 3:20 of the second period. He scored in front with a redirection of Mikko Rantanen’s cross-ice pass that went through the legs of St. Louis defenseman Tyler Tucker.
Duchene scored again 40 seconds later to make it 2-0 when his backhand pass into the crease intended for Jamie Benn caromed into the net off the skate of Blues defenseman Logan Mailloux.
Roope Hintz pushed it to 3-0 with another power-play goal at 18:06. He finished with a one-timer in the left circle off a pass from Robertson.
Blues forward Jake Neighbours left the game after the first period with a lower-body injury after blocking an Esa Lindell shot midway through the period, and St. Louis forward Jordan Kyrou left after the second period because of an upper-body injury.
