Three goals in 79 seconds spared the blushes after Jan Kostal and Jonas Hoog had given the visitors a shock lead.
But Phoenix rallied to win 6-3 and erase the memory of a 5-2 loss at Basingstoke on Saturday.
Last night, Kovar rammed home the first of his three in the sixth minute.
He latched onto a Tony Hand pass before the Wildcats turned it around to deservedly lead 2-1 at the end of the period.
Swindon could have had another early in the second and were left to rue missed chances when Michal Psurny added his 29th of the season.
The Czech fired the puck from behind the net and it somehow deflected in off Stevie Lyle’s pads in the Wildcats goal.
Stunned, Phoenix added two more; Richie Bentham firing ahead following Liam Chong’s great pass and Kovar launching a shot into the top corner.
Aaron Nell pulled one back three minutes into the third period but Psurny restored Phoenix’ advantage on the powerplay.
Kovar then notched his third to make it safe and give Phoenix a well-taken, if slightly flattering two points.
The result, if not the complete performance, was much-needed following a 5-2 loss at table topping Basingstoke the night before.
Phoenix started back-up netminder Paul Maudsley as number one Steve Fone was ill.
The youngster equipped himself well but Basingstoke took advantage and were four up by the 31st minute.
Jaroslav Cesky and Kovar gave Manchester hope in the third period but Tomas Karpov ended the contest on 52.23.
As Basingstoke lost their match on Sunday against the resurgent Telford Tigers, Phoenix lie two points behind them, with three games in hand.
To contact the author email: Mike.Appleton@prohockeynews.com or tweet @mascarandy