Paul Thompson's side won one game, drawn one and lost seven games against Belfast this season going into the match at the Odessy in Belfast.
The home side took the lead through Evan Cheverie on 4.12 and increased their advantage in the second period when Colin Shields netted from a Deniset assist on 23.14.
Blaze hit back and on 24.27, Adam Calder pulled one back, assisted by Hjalmarsson and Dan Carlson.
Shots continued to rain in on the Belfast goal and on a power play after 35.47, Sylvain Deschatelets scored to tie the game assisted by Cowley and O'Connor.
Those who had travelled to Northern Ireland were on their feet on 38.09 as Russ Cowley hit the third for Coventry from a Jon Weaver assist.
Into the third and Jon Weaver hit a fourth goal for The Blaze on 40.53 to give the Blaze a good victory.
Tomorrow night, the Blaze are at home to Edinburgh Capitals. Face off is at 6pm at the Sky Dome.