It was Saracens' third away win in a row, but it was an error-strewn game in which neither side played any fluent rugby of note.
Saracens deservedly won thanks to a dominant forward display and a calm performance by New Zealander Glen Jackson.
Leeds sorely missed a goal-kicker, with David Doherty missing an easy effort, and other kickable opportunities going to touch, where the aggressive Saracens defence held firm.
Iain Balshaw did his best to break the deadlock with some runs from deep, but they were also to no avail.
Saracens had chances of their own. Taine Randell and Cobus Visagie were both guilty of knock-ons close to the line, and Kyran Bracken was stopped just short, but finally Simon Raiwalui was driven over five minutes before the break.
The teams turned around separated by only those five points, but Jackson soon atoned for his conversion miss with a simple pemalty shortly into the second half.
Leeds lost a certain try when Tom McGee delayed the scoring pass to David Rees too long, and eventually threw it forward. Phil Christohers and Balshaw also threatened in Leeds' best spell.
But with another Jackson penalty putting Sarries eleven clear, and then yet another making it 14-0 with just ten minutes to go, the game was pretty much over as a contest.
A bonus point was still attainable, and David Rees' last-minute try gave Doherty a shot for it, but the kick was well wide, and Leeds left empty-handed.
For Leeds:Tries: Rees
For Saracens: Tries: RaiwaluiPens: Jackson 3
Leeds Tykes: 15 Iain Balshaw, 14 David Reeds, 13 Phil Christophers, 12 Chris Bell, 11 David Doherty, 10 Craig McMullen, 9 Alan Dickens, 8 Alix Popham, 7 Richard Parks, 6 Scott Morgan, 5 Tom Palmer (c), 4 Chris Murphy, 3 Rayno Gerber, 2 Rob Rawlinson, 1 Tom McGee. Replacements: 16 Ed Kalman, 17 Mark Regan, 18 Dan Hyde, 19 Colm Rigney, 20 Mark McMillan, 21 Tom Rock, 22 Rob Vickerman.
Saracens: 15 Mark Bartholomeusz, 14 Thomas Castaignede, 13 Kevin Sorrell, 12 Dan Harris, 11 Tevita Vaikona, 10 Glen Jackson, 9 Kyran Bracken, 8 Hugh Vyvyan (captain), 7 Ben Russell, 6 Taine Randell, 5 Iain Fullarton, 4 Simon Raiwalui, 3 Cobus Visagie, 2 Raphael Ibanez, 1 Kevin Yates.Replacements: 16 Matt Cairns, 17 Nick Lloyd, 18 Ben Broster, 19 Kris Chesney, 20 Ben Johnston, 21 Moses Rauluni, 22 Nicky Little.
Referee: Sean DaveyTouch judges: Brian Campsall, Don HelmeAssessor: Brian Leigh