Paul Adey's side won 2-0 at Hull on Saturday and 4-2 on Sunday night at their former coach Doug Christiansen's Sheffield Steelers.
Dustin Whitecotton scored in the first period against Hull and then Calvin Elfring sealed the win.
That put the Odyssey Arena side in a confident mood ahead of Sunday's game.
They raced 2-0 ahead of Sheffield, Jeffrey Szwez and Robbie Sandrock scoring.
It was 4-1 as Colin Shields and Whitecotton found the net before Sheffield retrieved a consolation.
All that means the Giants maintain their four point lead at the top of the table from the Dundee Stars and they are now seven points clear of Sheffield.
Next weekend it's a Scottish double for the Giants as they meet Edinburgh Capitals on Saturday and Fife Flyers on Sunday.