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.

Stuart Price, died on Sunday after colliding with a black Jaguar car in Colliery Lane, next to the junction with Murton Lane, in Easington Lane.
Northumbria Police said the Jaguar driver , who stopped his car - was left shaken but uninjured by the crash.
Mr Price, 24, of Murton, County Durham, was pronounced dead at the scene and police are appealing for witnesses.

The artwork at Clavell Tower, Kimmeridge Bay, Dorset, was hit by a boulder and cut off at the ankles in stormy weather.
The life-size figure was created to mark 50 years of UK building conservation charity Landmark Trust.
The charity said it was likely to be the "end of the road" for the work.
A spokeswoman said: "On Christmas Eve the Gormley sculpture at Kimmeridge Bay again succumbed to persistent heavy seas, this time presumably hit by a boulder hurled off the beach by the force of the storm.
"We are taking steps to recover the work imminently.
"It was always intended to have a relationship with the landscape and nature.
"Its position on this exposed stretch of Kimmeridge Bay has certainly brought that dynamic to the fore."
The trust said it did not yet know where the installation would be moved to, but that the "most important thing is removing it safely, given the weather, location, tide times, and holiday season".
John Bickerton, owner of Lulworth House B&B, found the statue during a walk with his family on Saturday.
He said: "We were sprinkling my mother's ashes on the far side of the bay before going round to take a family picture with the sculpture.
"We quickly realised it wasn't standing and when we got there could see it had sheared off at its thinnest point - the ankles. This time it looks like it might be fatal."
Sir Antony said he was "thrilled" when the sculpture toppled into the sea in September, calling it proof of its "dynamic relationship" with nature.
Chris Higgins scored twice as the Belfast Giants kept up their Elite League title challenge by defeating Coventry Blaze 3-0 on Sunday night.
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A cyclist has died in a collision with a car near Sunderland.
[NEXT_CONCEPT]
A conservation charity has said a cast iron sculpture by Sir Antony Gormley felled for the second time in just over two months will not be reinstated.