It was not a classic Tigers display, but they were superb in patches, only their distribution let them down, but their skills were much superior to a spirited Saracens team's.
The home side opened the scoring through the boot of stand-off Andy Goode when he kicked a simple penalty in the opening minutes.
Robbie Kydd levelled the scores at 3-3 with a penalty of his own after Tigers infringed at the breakdown.
Saracens went closest to the tryline in the opening exchanges, Simon Raiwalui threatening and knocking young centre Dan Hipkiss cold in the process.
However the Tigers defended tirelessly, and were eventually able to clear their lines after Saracens' Kevin Yates was whistled for a binding offence.
Still Saracens kept up the pressure, and were eventually rewarded with another Kydd penalty after an infringement at the breakdown.
Kydd then made the mistake that led to the opening try. He dropped a garryowen close to his line, and conceded a scrum.
Goode fed his backs with a perfect miss-pass and further passes from Sam Vesty and Hipkiss gave 19-year-old Tom Varndell another try to add to his recent impressive glut, which also gave the Tigers an 8-6 half-time lead.
Henry Tuilagi's bullocking running pressured Saracens into killing the ball shortly after the break, and Goode extended the lead with another penalty, and then landed another on 58 minutes for a 14-6 lead.
Substitute Glen Jackson kicked a long range penalty on 61 minutes to keep the visitors in touch at 14-9.
A scorching run by Simon Haughton for Saracens looked like it might result in a try for the visitors on 64 minutes, but Kydd was unable to hold on to a poor pass from the England sevens specialist.
A late try for replacement Smith, converted by Goode, sealed the win for the Tigers.
For Leicester:Tries: Varndell, Smith. Cons: Goode. Pens: Goode 3.
For Saracens:Pens: Kydd 2, Jackson