The win would have been more decisive had it not been for a last-minute try by Henry Paul to claim some scant consolation for the Cherry and Whites.
Alex Tuilagi's two second half scores put Leicester clear. The huge Samoan wing crossed the line in the 54th and 74th minutes after Gloucester had been battered by a fearsome Leicester pack performance.
It could have been a lot worse for Gloucester as well. The Tigers had one score ruled out and Martin Johnson held on at a crucial moment when an overlap was screaming for a pass.
Both sides made a raft of injury-enforced changes before the game, the most significant of which were the injury-enforced absences of Harry Ellis and Andy Gomarsall
Gomarsall suffered a back spasm in the warm-up while Ellis was given more time to recover from a sore Achilles tendon.
The absence of Gomarsall and Duncan McRae left Gloucester with a new and barely-heard-of half-back pairing of Alex Page and Brad Davies.
Leicester, though, looked equally unfamiliar in the back line, where 19-year-old Tom Varndell made his debut on one wing with the relatively untried Dan Hipkiss, 21, on the other.
The game saw a mighty forward battle, including Lewis Moody's test against understudy Andy Hazell.
Gloucester managed a furious early surge from a driven lineout and Marcel Garvey's thrust down the left, and landed the first blow with Paul's third minute penalty.
The rest of the half belonged to Leicester as they gradually won the forward battle, then launched Rabeni to devastating effect into midfield.
He showed all required centre skills with the 12th minute try that saw him break past Paul 40 metres out and then surge between two defenders to the posts for his eighth try this season.
Goode converted, then added a penalty to make it 10-3, although Leicester could not quite crack Gloucester's rugged defence after that.
The visitors dug in by making three times as many tackles as their opponents and closed the gap against the run of play with a second Paul penalty before the break.
Gloucester, though, conceded a penalty immediately after the interval and were starting to feel the pressure in the tight. Goode slotted the kick for a 13-6 lead.
Hipkiss got over the line for the Tigers on the right, only for the score to be ruled out because of Vesty's forward pass in another Rabeni-inspired build-up.
But Johnson made no mistake when he popped up in midfield from their next attack, providing the perfect assist for replacement wing Alex Tuilagi to outstrip the cover from 30 yards for the clinching try just before the hour.
After Goode stretched the lead with his third penalty, Gloucester had to throw caution to the wind to rescue even a bonus point.
All they could manage was to hand Leicester another gift. Garvey's pass was picked off by Tuilagi, who blasted 70 yards down the right-hand touchline to score.
Paul's consolation try and conversion made the scoreline look more respectable but Gloucester were well beaten.
For Leicester:Tries: Tuilagi 2, RabeniCons: Goode 2Pens: Goode 3
For Gloucester:Try: PaulCon: PaulPens: Paul 2