Cooper's double came either side of a rapid-fire three-goal spell in the second period that saw Sam Ruopp, Grant Cooper and Bast all score within three minutes and one second to secure the win, with netminder Tyler Beskorowany producing another win.
The Flyers had the better of the early chances and Dillon Lawrence nearly surprised Beskorowany when he spun and shot on the backhand, before Liam MacDougall shot straight at the netminder after a giveaway at the blue-line.
But when the first powerplay opportunity presented itself to the Giants they were lethal, Mark Cooper holding the puck in the right circle and sniping one into the top corner over the shoulder of Shane Owen at 7:23. (0-1)
It looked like the Giants would make it to the first intermission ahead, but two late penalties to Matt Foley and Scott Conway - both for interference - put them on the penalty kill and, although they killed off the former's, a nice passing move involving Chris Lawrence and Zack Phillips allowing Janne Laakkonen to tap in for the equaliser at 18:56. (1-1)
The Giants were unable to capitalise on an early powerplay in the middle frame as Laakkonen sat for tripping, but once they got going they hit the Flyers with a quickfire triple salvo that put the game to bed.
The first came at 29:32 as Matt McLeod drove the net and got the backhand shot off and, although Owen saved initially, Ruopp was there to supply the finish (1-2), quickly followed by Grant Cooper forcing the puck home in a scramble at the crease at 31:44 for the third. (1-3)
And when Reece Cochrane was called for hooking shortly after, Bast took full advantage when he ripped a one-timer in from the high slot for the powerplay goal at 32:33. (1-4)
The Giants survived an early scare in the final period as a slack play in neutral ice allowed Brayden Sherbinin to skate in on goal and his backhand looked to have beaten Beskorowany on the backhand, only for the video review to determine he actually hit the crossbar and not the interior of the goal.
Fife kept pushing, however, and they were helped when Bast was called for interference midway through the period, but the Giants, led by Beskorowany, shut the door on the penalty kill to keep their three-goal lead.
But a spearing call on Grant Cooper and a face-off violation against Donovan Neuls put the Giants on a 5-on-3 kill late, with the Flyers adding another skater as they pulled Owen, and they made it a nervy finish as Kamerin Nault poked in Laakkonen's pass with 1:40 remaining. (2-4)
However, any nerves were settled by Mark Cooper, who notched his second goal of the night by sliding the puck into the empty net with 16 seconds remaining to ensure it would be a four-point weekend for the visitors. (2-5)
Next up, the Stena Line Belfast Giants return to a sold out The SSE Arena, Belfast to take on the Fife Flyers in the Challenge Cup Final on Wednesday 01 March 2023.