Higgins found the net near the end of the second period and Steve Saviano made it 2-0 in the third period, Higgins then completing the scoring.
The victory completed a good weekend for the Giants, who beat Nottingham Panthers 7-4 in Belfast on Saturday.
Derrick Walser's side now prepare for a busy schedule of Christmas fixtures.
That sequence begins with the second leg of their Challenge Cup quarter-final against Manchester Storm at the SSE Arena on Tuesday evening, the score standing at 3-3 after the first leg.
Edinburgh Capitals are the visitors to Belfast for back-to-back games on Thursday and Friday.
Sunday's triumph saw the Giants close the gap on league leaders Cardiff Devils to eight points, with Belfast having two games in hand.
Stephen Murphy started in the Giants net while Ryan Martinelli sat out the game through injury.
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Three goals in the third period saw the Giants take victory on Saturday, with Colin Shields, Blair Riley and Chris Higgins all on target.
The Giants led 3-2 after the first period but the Panthers were level at 4-4 after the second period of play.
Brandon Benedict, Jim Vandermeer, Alex Foster and Riley were the Giants' scorers in the opening two periods.
Jeff Brown grabbed a double for the visitors, with Brian McGrattan and Dan Spang also finding the net for Nottingham.
Chris Higgins scored twice as the Belfast Giants kept up their Elite League title challenge by defeating Coventry Blaze 3-0 on Sunday night.