Needing to win by three clear goals after losing 4-2 in the first leg, Paul Thompson's side went a goal down after only 51 seconds through Greg Chambers to delight the 275 strong travelling support.
A full strength Coventry Blaze side hit back through Sylvain Cloutier and Dan Carlson (8.10) to lead at the end of the first period.
Basingstoke scored in the fifth minute of the second period through Brad Cruckshank. That was the only goal of the period.
In the fifth minute of the third period, Danny Stewart scored his 22nd goal of the season in the fifth minute to put Paul Thompson's side back in front.
Four minutes later, it was all square and game very much on when Adam Calder scored. Dan Carlson, assisted by Adam Calder, made the most of a loose puck and slammed home to send the Blaze nap in the 14th minute.
With 3.20 left, Curtis Huppe got round the net minder to slot home and give Blaze a 6-2 victory and an 8-6 aggregate victory.
Blaze travel to Basingstoke on Saturday for an Elite League game.