A try from 22-year-old fullback Jon Goodridge got the hosts off to a good start midway through the opening half after a Henry Paul penalty.
Paul converted and added a second penalty before the interval for a 13-0 half-time lead.
Saracens then got themselves back into the game when former All Black captain Taine Randell crossed the line for a try four minutes into the second half, with fly-half Andy Goode adding the extras.
But it was to be Sarries' last scoring play as Gloucester turned the screw – Goodridge grabbing a second try on the 52 minute mark as Paul again converted.
Former England wing James Simpson-Daniel then got a third only three minutes later as the result went beyond doubt, and then replacement flanker James Forrester guaranteed the bonus point when he went over with 12 minutes to go for coach Nigel Melville's men.
For Gloucester:Tries: Goodridge 2, Simpson-Daniel, ForresterCons: Paul 2Pens: Paul 2
For Saracens:Try: RandellCon: Goode