At the Metroradio Arena in Newcastle, Coventry, trailed to goals either side of the end of the first period.
On a 25.31 power play for interference from Rankin, Danny Stewart pulled one back with assists by Barrie Moore and Corey LeClair.
The Blaze support who had journeyed up to the North East were back on their feet when assists by Jon Weaver and Jon Coleman set up Dan Carlson to score.
Another power play in the 30th minute saw Jon Weaver give the Blaze the lead for the first time in this Elite League match.
The win was completed in the third period after 42.39 by Adam Calder firing in from assists from Dan Carlson and Scott Kelman.
Next Saturday, Coventry Blaze travel to Hull Stingrays before taking on Nottingham Panthers at the Sky Dome on Sunday.
On Boxing day, the face off at Cardiff Devils has been brought forward to 6pm.