Francis Pare, Gustav Nyquist and Joakim Andersson all had a goal and an assist for Grand Rapids (15-9-2), while Petr Mrazek made 29 saves for the win.
Landon Ferraro, Ray’s son, had two assists for the Rapids.
Defenceman Nick Tuzzolino had his first goal of the season for Abbotsford (15-7-6).
Barry Brust started in net for the Heat, making 14 saves on 16 shots over two periods. Danny Taylor stopped eight-of-10 shots in relief.
The Griffins went 2-for-3 on the power play and Abbotsford was 0-for-2 with the man advantage.
There was a flurry of scoring in the final few minutes of play, as Sheahan scored on the power play with 3:58 left in the third.
Tuzzolino replied 44 seconds later and then Nyquist had an empty-net goal with just over a minute left on the clock.