But the home side were made to struggle for the victory, the West Country visitors matching their hosts for much of the 80 minutes.
Boosted by the return of talismanic England back Mike Catt, Bath tore into the Tigers in the opening exchanges of the game, taking the lead through a penalty by fullback Ollie Barkley.
Leicester had a swift opportunity to level the scores with a penalty of their own some moments later but fullback Tim Stimpson made an uncharacteristic error with the 35 metre kick.
Barkley stretched Bath’s lead with another penalty and, despite a number of promising incursions into their opponents’ territory, Leicester were unable to put any points on the board for most of the first-half, Healey missing with a drop-goal and Stimpson again off-target with another penalty attempt.
Then, just before half-time, back rower Martin Corry ended the Tigers’ points drought, crashing over for a try after some good work by Neil Back.
That made it 6-5 at the break and Leicester soon took the lead in the second half as Stimpson at last found his range with a penalty kick at goal.
Leicester made a crucial breakthrough as hooker Dorian West touched down, Stimpson adding the conversion.
With Catt finding himself in the sin-bin for a ten minute spell following an illegal challenge on Corry, Leicester took advantage of their extra man, Back latching onto the ball during a forward drive to score a try – again converted by Stimpson.
Bath fought back as the clock ran down, Kevin Maggs and Mike Tindall scoring tries, both converted by Barkley.
But Leicester were able to hold on for the narrow two-point victory.
For the Leicester Tigers:Tries: Neil Back, Martin Corry, Dorian WestPens: Tim StimpsonCons: Tim Stimpson (2)
For Bath:Tries: Kevin Maggs, Mike TindallPens: Ollie Barkley (2)Cons: Ollie Barkley (2)