Leon Lloyd's first-half try proved the difference as Leicester warmed up for next week's Heineken Cup quarter-final against Bath with victory at The Rec.
Bath (9) 12:
Pens: Malone 4
Leicester (16) 19:
Pens: Goode 4
Andy Goode was also key for the Tigers, emerging from England's disappointing Six Nations defeat to Ireland last week with 14 points to steer them home.
The Tigers enjoyed a fine start in the wet conditions but two Goode penalties were equalled by Chris Malone.
But Goode set up Lloyd for his score to seal it despite a late goal apiece.
Bath battled aggressively on a stamina-sapping surface, but despite four Malone's penalties securing them a losing bonus point, they could have no complaints about the result.
Leicester welcomed back four of their England stars from Six Nations duty as Goode, Lewis Moody, Harry Ellis and Martin Corry all returned, while Bath included red rose trio Lee Mears, Steve Borthwick and Danny Grewcock.
And it was Goode who produced the game's crucial piece of quality to effectively settle the tie.
The 25-year-old made the crucial intervention during a sustained Leicester attack to float out a high-class scoring pass to an unmarked Lloyd in the corner.
Leicester were full value for their advantage but Bath hit back with a penalty before the break, mounting a searing raid into the Tigers' 22 that ended with Moody being sin-binned for deliberate offside and Malone completing his hat-trick.
But the visitors continued to control the game and, despite Corry spilling a late chance when he looked odds-on to score, they were able to see out a comfortable win to keep themselves firmly in the title play-off picture.
Bath coach Brian Ashton
"We didn't think very clearly in those conditions.
"It wasn't a very good game of rugby. Both sides played pretty poorly, but we played more poorly than Leicester did and were less intelligent in those conditions.
"There was a massive lack of intensity there today - and to be honest, we had been a bit flat in the week as well."
Leicester coach Pat Howard
"Conditions made it tough out there, but I thought we were reasonably controlled.
"I thought our forwards played particularly well, and sometimes you have just got to go out there and play the conditions.
"As far as Andy Goode is concerned, his control and maturity is growing - and if he wants to challenge for an England spot he has got to continue with that all-round game."
Bath: Stephenson, Finau, Higgins, Maddock, Bory, Malone, Walshe, Flatman, Mears, Bell, Borthwick, Grewcock, Beattie, Lipman, Delve.
Replacements: Abendanon for Stephenson (70), Williams for Walshe (70), Filise for Flatman (60), Dixon for Mears (70), Short for Grewcock (60), Fea'unati for Lipman (71).
Not Used: Dunne.
Leicester: Vesty, Murphy, Smith, Hipkiss, Lloyd, Goode, Ellis, Rowntree, Buckland, White, Kay, L. Deacon, Jennings, Moody, Corry.
Replacements: Healey for Ellis (74), Skinner for Jennings (77).
Not Used: Taikaufa, Holford, Cullen, Cornwell, A. Tuilagi.
Sin Bin: Moody (36).
Ref: Chris White (RFU).