Sam Olver put the visitors in control in the first half, kicking a couple of early penalties before diving over for a try just before the half-hour mark.
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David Strettle kept Saracens in contention though, bursting down the wing before squeezing over in the corner to score Saracens' only points of the first half.
Mike Ellery cut Northampton's lead to a single point within a minute of the restart, making the most of a quick break by the hosts to add their second try of the afternoon.
The result sees Saracens through to next weekend's final, where they will face the winner of tomorrow's last-four clash between Leicester Tigers and Exeter Chiefs.