The four-try win means Bath top pool three with a perfect record of four wins from four games, while two-time champions Leicester crashed out of the competition after finishing behind Sale and Exeter in pool two.
It was Leicester's third successive defeat in all competitions, their second at home.
Bath scored two tries in each half to earn a bonus point and after leading 18-17 at half-time they dominated the second period, winning it 17-0.
Rugby
Ospreys snatch win with late Rhys Webb double
30/04/2016 AT 15:46
Their tries came from Alafoti Fa'osiliva, Matt Banahan, Ollie Devoto and Carl Fearns while Gavin Henson kicked 15 points.
Leicester, who had George Chuter sin-binned at the start of the second half, replied with tries from Pablo Matera and Blaine Scully, with Owen Williams kicking seven points.
Newcastle ended their LV= Cup campaign on a high note with a 29-0 win over Newport GwentDragons at Kingston Park.
On a gluepot pitch both sides displayed surprisingly good handling in the first half but the Falcons dominated the possession and ran in four tries, three of them before the break, as Newport struggled to match them up front.
It was different story after the break the game disintegrated on the back of myriad changes from the benches and any hopes Newport may have had of a comeback were dashed when they had centre Nic Cudd sent off for a spear tackle on Adam Powell in the 56th minute.
Sam Davies kicked a last minute touchline conversion to end Sale Sharks' hopes of reaching the semi-finals and give Ospreys a 37-36 win at Bridgend.
The English club needed a bonus point win to reach the last four and they looked on their way as they led 28-13 at the break.
However, the Ospreys bounced back from 36-20 down after 55 minutes - with wing Aiesa Natoga to complete a try-hat-trick.
A five-try 35-5 win over Harlequins was not enough to take the Cardiff Blues through to the semi-finals.
Harlequins were in many ways the architects of their downfall. Their ambition was admirable, but their handling frequently let them down at vital moments.
Rugby
Cardiff Blues maintain European Champions Cup qualification hopes with home win
17/04/2016 AT 16:11
Rugby
Cardiff Blues maintain European Champions Cup qualification hopes with home win
17/04/2016 AT 15:44