Mouillierat scored with a forehand-to-backhand deke, and Jaffray showed patience with a toe-drag before scoring top shelf.
The Bruins opened the scoring through Johnson, who buried a one-time slapshot from the face-off dot 8:18 into the first period during 4-on-4 play.
Lowry equalized for the IceCaps, tipping home a Blair Riley slapshot from the point with 1:51 left in the first.
Just 3:44 into the second period, Postma found space in the slot and ripped a wrist-shot hard and low, which deflected off Gordon.
Khokhlachev tied it for the Bruins, beating IceCaps goalie Eddie Pasquale five-hole with a wrist shot from a wide angle at the 14:16 mark of the second.
Postma gave the IceCaps a 3-2 lead with a wrist shot from just inside the blueline that Bruins goalie Malcolm Subban misplayed with his glove with 1:08 remaining in the second.
At the 6:32 mark of the third period, St. John's turned the puck over on its blue line while on the power play and Randell scored backhand, low blocker on a partial breakaway.
Pasquale made 30 saves for St. John's. Subban stopped 29 shots for Providence.
The IceCaps went 1 for 6 on the power play while the Bruins failed to score on four chances with the man advantage.