In Belfast, Paul Thompson's team held the home side in the first period but two minutes into the second as penalties for Szwez and Derek Campbell expired, Belfast scored through Nova Scotian Brandon Benedict.
That lead only lasted until 35.41 when Greg Chambers slipped the puck to Adam Calder who made no mistake with a powerplay goal.
Blaze grew in strength and nine minutes into the third period, a penalty to Blaze was thumped into the net by Adam Calder, delighting those who had travelled to Ulster and those watching back in Coventry, via the Blaze's bar at Crosbys.
On Sunday night, the Blaze are at home to Hull Stingrays.
.