Harlequins dominated from the outset and Burke claimed an early lead with a long-range penalty in the fifth minute.
Burke continued to stamp his authority on the game and he was back in the thick of it when he heaved a kick across to the left-wing for flyer Ugo Monye to gather, split the defence and rush over for the try. Burke then stretched the lead with the conversion and added another penalty to open the gap even further as a shell-shocked Saints could only look on.
The hosts continued to dominate and heaped on the pressure – Monye and then right-winger Simon Keogh both threatened to break through – but it was the Quins pack, who would claim the next try after driving for the line, with Pat Sanderson on hand to dot down.
Samoan hooker Tani Fuga barged his way over just before the break to put the game well clear of the Saints, but when Quins No.8 Tony Diprose was sin-binned, the visitors took advantage with a try to lock Rob Hunter to close the gap at half-time.
Quins soon put the game out of Northampton's reach after the break, however, when Diprose made up for his error with some hard work to set the ball up for his backs to move it out wide, sending Keogh over in the corner.
Keogh sealed the win 12 minutes from time when he raced over for his second of the game after being put into space, stretching the lead to 43-7.
Two late Northampton tries through Andrew Blowers and Grant Seely did little more than flatter the visitors, who had effectively been put away long before.
For Harlequins:Tries: Monye, Sanderson, Fuga, Keogh 2Cons: Burke 2, DunnePens: Burke 4
For Northampton:Tries: Hunter, Blowers, SeelyCons: Drahm 3