Bath opened the scoring with two minutes of the match played, when Olly Barkley kicked a sweetly struck penalty. Tigers hit back almost immediately however, as Andy Goode replied with three points of his own.
Bath then re-took the lead after six minutes when Steve Borthwick made the most of a glaring overlap to put the West Country side 8-3 in front.
Again Tigers responded in the perfect manner, with Scott Bemand scoring a fantastic individual try. The England tourist picked up from the base of the scrum 35 metres from the Bath line, before cutting inside Joe Maddock to race through. Goode's impressive conversion gave Pat Howard's side a 10-8 lead.
Unfortunately for the visitors, the advantage was short-lived, as the lead swapped hands again with 14 minutes on the clock - Olly Barkley's second successful penalty of the afternoon giving Bath a one-point cushion at 11-10.
The home team then found themselves down to 14 men, after referee Dave Pearson sent Danny Grewcock to the sin-bin with 27 minutes gone. The Lions second row was rightfully penalised for deliberately diving over the top as Tigers looked for quick possession only metres short of the Bath line.
Goode ensured Grewcock paid in full for his misdemenaur by slotting his second penalty of the afternoon.
Martin Castrogiovanni then received identical punishment just after the half hour mark for a similar offence, with Barkley following Goode's example by kicking the resulting penalty.
A piece of individual magic from Tigers' Sam Vesty then silenced the boisterous home crowd. The England Saxons full back showed great imagination to fire over a long-range drop goal, when there appeared to nothing on the cards.
Barkley's fourth successful penalty saw Bath regain the lead after 31 minutes, but Goode edged Tigers back in front two minutes later. The England number ten then increased Leicester's lead to five points at 22-17, courtesy of another well-taken penalty.
Barkley then failed to cut the half time deficit to two points, as his late penalty attempt drifted narrowly wide of the left hand upright.
It was Tigers who had the opportunity to strike first in the second period, but this time it was Goode who failed to take advantage, as his penalty struck the same post.
Louis Deacon became the next victim of Pearson's notebook, receiving the third yellow card of the match with 47 minutes played.
Bath immediately made the most of their numerical advantage, with no.8 Zak Feaunati being driven over by his fellow forwards. Barkley added an assured conversion to give Bath the lead at 24-22.
Tigers hit back six minutes further down the line as Goode kicked his sixth penalty of the match to put Tigers 25-24 in front.
The home side then went close to registering their third try on 58 minutes, when Chris Malone's cross-field chip just evaded the grasp of Shaun Berne.
Bath did re-take the lead three minutes later however, as Barkley slotted his fifth three-pointer after Tigers were penalised for a scrummaging infringement.
Barkley then missed the chance to edge his side further in front with 64 minutes on the clock, following Pearson's decision to penalise Seru Rabeni for an illegal tackle. It was a different story two minutes later when Goode was adjudged to have caught Barkley with a high tackle and Malone made no mistake with his first penalty of the afternoon.
Tigers then received a further set-back with nine minutes remaining, as Henry Tuilagi left the field through injury. For the second successive match, Tigers were forced to play one of their squad out of position in the back row. This time it was Matt Cornwell who shifted to the flank, with Matt Smith moving into the centre.
There was more bad news for Leicester a minute later, as replacement Dan Hipkiss became the third Tigers player to receive a yellow card from Pearson.
To make matters worse, Barkley kicked the ensuing penalty to give Bath an eight point lead at 33-25.
Things continued to go downhill for the away side as England U-21 international Nick Abendanon finished off a flowing move to leave Tigers trailing by 13 points.
Bath then clinched their first win of the season with the final play of the match, when Joe Maddock crossed after good hands from the Bath backline.
