Sarries went ahead via a penalty try from a driving maul, with two Freddie Burns penalties for Tigers either side, as the hosts led 7-6 at the break.
Replacement hooker Jamie George bundled over to extend Saracens' lead.
Saracens added two more penalty tries as their forwards dominated to make it 12 straight wins in all competitions.
Mark McCall's Sarries now hold a six-point lead at the top of the table over Exeter, while Leicester succumbed to just their second loss of the season.
After a scrappy first half in difficult conditions, the Saracens pack provided a masterclass after the break as they became the first side in Premiership history to be awarded three penalty tries.
England international George started Sarries' second-half dominance when he dotted down at the end of a rolling maul.
As the hosts began to camp themselves in Tigers' 22, referee Greg Garner awarded Sarries their second penalty try following a collapsed scrum.
Saracens sealed the bonus-point win with a third penalty try following more fine work from the pack shortly after Tigers' England prop Dan Cole was sent to the sin-bin, before closing out the game in the final 10 minutes.
Saracens: Goode; Ashton, Bosch, Barritt (capt), Wyles; Hodgson, Wigglesworth; Vunipola, Brits, Du Plessis, Itoje, Kruis, Rhodes, Fraser, B Vunipola.
Replacements: George, Gill, Lamositele, Hamilton, Wray, De Kock, Farrell, Taylor.
Leicester: Veainu; Camacho, Tait, Bai, Goneva; Burns, Harrison; Ayerza, Thacker, Balmain, Barrow, Kitchener, Slater (capt), Croft, Pearce.
Replacements: T Youngs, Mulipola, Cole, Fitzgerald, McCaffrey, B Youngs, Williams, Thompstone.
Sin-bin: Cole
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Premiership leaders Saracens made it eight wins from eight as they earned a bonus-point victory over Leicester at a wet and windy Allianz Park.