But despite leading 19-9 early in the second half, the Watford club had to withstand a monumental effort from the Tigers as they put together 32 phases but failed to breach the Sarries line.
Leicester, for whom Toby Flood kicked all the points, were awarded a penalty at the death but were penalised for holding on at the ensuing ruck allowing Owen Farrell to boot the ball out to end the match.
Saracens had struck the opening blow of the game when Farrell capitalised on a Ben Youngs indiscretion which saw the England man sent to the sin bin after just six minutes for cynically killing the ball.
But despite being a man down, Leicester responded immediately earning themselves a penalty which Flood duly converted.
Upon Youngs' return Leicester took the lead for the only time in the match, only to relinquish it straightaway as Flood and Farrell exchanged penalties.
Sarries then scored the only try of the game, Brits making a trademark charging run before drawing in the Tigers' defence and releasing Short to finish in style, Farrell adding the extras.
Flood brought Leicester back to within a converted try at the break with another penalty, but Farrell managed to stretch Sarries' lead back to ten points when the Leicester scrum was penalised.
The Tigers inched their way back into the game thanks to two more Flood penalties while Farrell added a further three points with ten minutes remaining.
With five minutes to go, Flood got Leicester to within four points, but despite huge pressure at the death, Sarries held out to secure a historic victory.