The visitors required a last-minute try in extra time to get the better of Saracens when the sides met in last season's final, but it looked like being a far more comfortable encounter when James Wilson touched down shortly after kick-off.
Luther Burrell surged through the home defence before sending the ball out wide for wing Wilson to go over - Stephen Myler adding the extras.
Charlie Hodgson responded with a penalty for Saracens, but Mark McCall's men were 25-3 down by the time they next registered any points.
Wilson got on the end of a Lee Dickson punt to claim his second try, before Phil Dowson barged over from close-range and Myler took his tally to 10 points for the half.
Jackson Wray's score in the closing stages of the opening period gave Saracens some hope to cling on to, and Saints were much improved after the interval.
Hodgson and Myler traded penalties before Chris Wyles capitalised on Alex Waller's sin-binning - going over twice in the corner.
Hodgson missed both conversions, but his late penalty did, at least, earn Saracens a losing bonus point, while Saints now sit two points clear of Exeter Chiefs at the summit.
Exeter briefly went top of the Premiership following a 31-15 victory over Wasps on Saturday.
Like Saints, Exeter did the damage in the first half, with England international Jack Nowell touching down twice as the home side moved into a 25-8 lead at the interval at Sandy Park.
Tom Lindsay scored the only try of the second 40 minutes, but it was too little, too late for Wasps as Exeter held on for the win.
Second-placed Exeter sit level on points with Bath, who were 33-23 winners at London Irish on Saturday - Gavin Henson making a contribution of 18 points with the boot.
London Welsh remain winless courtesy of a 26-5 home defeat at the hands of Leicester Tigers on Sunday.
Nick Scott opened the scoring for Welsh, but it proved to be their only score of the match, as Leicester - not at their best - recovered to grind out a win.
On Friday, Sale Sharks climbed above Harlequins with a 16-12 win on the road, while Newcastle Falcons registered their third win of the season - beating Gloucester 20-10.