It was actually Newcastle who had been first out of the blocks, wing Liam Botham kicking a long-range penalty to put his side up by 3-0 in the fifth minute.
But Saracens struck back with Andy Goode – an early replacement for starting fly-half Tim Horan – opening his side's account with a straightforward penalty kick.
The home side went into an 8-3 lead following some excellent driving play from their pack, hooker Matt Cairns able to ground the ball for the try following a lineout steal close to the Newcastle line.
Samoan fly-half Earl Va'a clawed back another three points for the visitors in first-half injury time with Newcastle's second penalty, but that three-pointer was immediately cancelled out by Goode to make it 11-6 at half-time.
Goode slotted a drop-goal in the second half to inch his side further ahead but Newcastle were not finished yet, launching a barnstorming attack that saw flanker Epi Taione over for a try.
With Va'a converting, the score was balanced at 14-13 in favour of the home side with the clock running down.
With both sets of fans on the edge of their seats, Saracens drove upfield to put Goode in position for his second successful drop-goal to seal the victory.
Saracens:Tries: Cairns. Pens: Goode (2). Drop Goals: Goode (2).
Newcastle:Tries: Taione.Cons: Va'a.Pens: Botham, Va'a.