The Challenge Cup match in Belfast should have gone into sudden death overtime, and penalties if necessary, to determine the winning team.
Overtime will now be played ahead of the league game between the sides.
The Elite League apologised for "an on-ice error and  any inconvenience caused to supporters".
Craig Peacock, Mitch Ganzak on the powerplay and Colin Shields were the scorers for the Giants in Friday night's encounter.
Craig McCallum, Ryan Hayes and David Rutherford were on target for Capitals.
The Belfast Giants-Edinburgh Capitals game will be finished on Saturday night after match officials wrongly called the match over after a 3-3 draw.