The game was tied at 1-1 when Pietrangelo put a wrist shot past Devan Dubnyk to give the Blues the lead for good.
Matt D'Agostini and Brad Boyes scored for St. Louis 1:27 apart in the second period to give St. Louis a 4-1 cushion.
The Blues got 29 saves from Ty Conklin to end a four-game losing streak. Edmonton has lost three in a row and eight out of nine.
Conklin gave up goals to Taylor Hall and Theo Peckham during the latter stages of the second period, allowing Edmonton to climb within one. Brad Winchester gave St. Louis some insurance by scoring the only goal of the third period 5:58 into the stanza.
Dubnyk gave up all five St. Louis goals on 26 shots.