The home side hit back, however, and two tries courtesy of Samu Manoa in the second half gave Northampton a lead to hold on to in the closing stages, which the Saracens were unable to claw back.
An in-form London Wasps were comfortably beaten by Gloucester Rugby 36-5 at the Kingsholm Stadium courtesy of four tries shared by Matt Cox and Henry Trinder, and a further five points from Dan Murphy late on.
A Cook penalty added to the Gloucester scoring as they saw off a Wasps side who had won eight of their last nine games.
Elsewhere, Exeter Chiefs picked up their third successive cup win in as many weeks after convincingly beating Worcester Warriors at Sixways Stadium.
Haydn Thomas's two tries after 68 and 77 minutes, combined with a try for Ceri Sweeney with seconds remaining, rounded off the scoring for Exeter against a down-and-out Warriors, with the contest ending 42-3 in favour of the away side.