Leicester went down to their fourth consecutive defeat in this season's LV= Cup in a highly controversial contest at Welford Road which saw home hooker Rob Hawkins sent off.
The Tigers finished pointless in their group, with a bonus-try win for Bath keeping alive their slim hopes of progressing to the semi-finals.
Nick Scott, Ed Slater, Simon Taylor and David Barnes crossed for Bath's tries.
Leicester were dealt an early blow when Hawkins was yellow-carded for punching within two minutes, but Bath took no advantage of the hooker's absence as the Tigers had the better of that 10-minute period with Thomas Waldrom making a couple of powerful bursts.
The opening quarter was a competitive affair but scoreless, with the game frequently interrupted by the award of penalties or injuries.
One of the injuries was suffered by Bath's young centre, Ben Williams, who left the field in a groggy condition.
Bath, with the likes of Danny Grewcock, Duncan Bell and Taylor in their forward line-up, had the superiority in the scrums with the Tigers conceding frequent penalties in that area.
The visitors were able to build a platform in the Tigers 22 and from a line-out they sucked in the home defence to leave Scott with a simple run in for the opening try after 23 minutes, with Sam Vesty kicking the conversion.
Leicester were soon on the score-sheet. From deep inside his own 22, Jeremy Staunton neatly chipped over the Bath defence, Matt Smith kicked on but was tackled, however it mattered not as Lucas Amorosino collected the loose ball to race away and score.
The game burst into life, and another try followed as the lively Tom Biggs finished off another excellent passing movement from Bath to extend their lead.
Almost immediately back came the Tigers to level the scores, with Dan Hipkiss being the main contributor to a splendid try.
The centre, who is due to join Bath next season, first fended off two defenders on a storming touchline run and fed Waldrom, before Hipkiss featured again to evade two more Bath players and allow Slater to pick up and score. Staunton converted with a fine kick to tie the scores.
On the stroke of half-time Hawkins was sent off by Welsh referee James Jones for using his elbow in a tackle.
The hooker was initially shown a yellow card but it was his second of the night so it soon became red.
The Tigers lost Matt Smith with a leg injury but despite being a man down they matched their opponents with the third quarter being scoreless.
Eventually numerical advantage told and with 14 minutes remaining Taylor drove over from a close range scrum for a try which Vesty converted.
Waldrom was then yellow-carded and the remaining 13 could not prevent Barnes grabbing a late try to secure Bath's bonus point.