Lucas Guillaume was shown a yellow card after eight minutes to give Saracens an early advantage.
Tigers fought back after the break, with two tries in three minutes giving hope to the visitors.
Andy Saull got the fourth try for Saracens, opening up a 21-point lead for the home team.
Harry Thacker scored a third for Leicester in the last minute.
Matt Cornwall added the extra points with the conversion in the final action of the game.