The slow-starting Sarries, who conceded 10 points in the opening four minutes of the 25-15 defeat at Sale in their previous match, were 10-0 down again after only 13 minutes.
Tykes and Scotland fly-half Gordon Ross kicked a third-minute penalty and added the conversion after left-wing Tom Biggs scored an excellent try.
The Leeds Metropolitan University student marked his recall to the side by taking beating Saracens fullback Dan Scarbrough, his former Leeds clubmate, standing as he went round him and crossed in the corner.
Saracens hit back when they took the ball off the end of a line-out and slick handling by scrum-half Alan Dickens, Ross and centre Andre Snyman sent left wing Paul Bailey over in the corner.
Fiji fly-half Nicky Little converted from the touchline but was then off target with a straight penalty 40 metres out.
His opposite number Ross stretched Leeds 19-7 ahead by half-time with three penalties to take his first-half tally to five successes from five kicks.
Saracens paid the penalty for their indiscipline as Ross punished them for a ruck infringement, a high tackle by Little on Dave Rees and an obstruction.
A more determined start to the second half saw Saracens, who had hardly figured as an attacking force before the interval, turn pressure into points as Little kicked three penalties, to one from Ross, to reduce the deficit to six points.
But Leeds, with former England full-back Tim Stimpson – sidelined by a knee injury since his close season signing from French club Perpignan – making his debut as a second-half replacement, repelled their attacks.
Leeds came again in the 74th minute when Snyman, South Africa's most capped centre, took a pass from Ross and turned through Little's tackle to crash over by the posts for a try which Ross converted to stretch the lead to 29-16.
Saracens launched a last-ditch assault but a superb tackle by young Biggs, which stopped centre Ben Johnston in full flight, combined with some poor handling and over-elaboration in attack, kept Saracens at bay until the seventh minute of injury time.
Leeds eventually cracked when Little crossed for the second Saracens try, which he converted, but it was too late to save the home side from their second successive defeat.
For Saracens:Tries: Little, Bailey Cons: Little 2 Pens: Little 3
For Leeds Tykes:Tries: Snyman, Biggs Cons: Ross 2 Pens: Ross 5