George Ford kicked all Bath's points, but t was a game far removed from their previous meeting two weeks ago, with Exeter taking the game to Bath from the off.
When a Chiefs player was tackled off the ball just outside Bath's 22 with five minutes on the clock, Chiefs fly-half Gareth Steenson kicked a penalty to make it 0-3 to the visitors.
George Ford was given the opportunity less than four minutes later to level the scores after the Chiefs were deemed offside in their attempt to scramble after a loose ball - one he took well to make it 3-3.
In the 22nd minute, Chiefs fullback Luke Arscott received a long kick from Ford. Realising that it was all Bath forwards out wide, he exploited the opportunity, second row Damian Welch doing well to reach over to score in the corner. Steenson missed with his conversion attempt, but Exeter led 3-8.
After some strong showings in the scrum from Bath, Ford banged over a penalty with eleven minutes remaining to bring his team within two points of Exeter. 6-8 to Chiefs.
In the final minute of the first half, and just when Bath needed it most after some relentless attacking phases from Exeter, Ford showed tremendous power with the boot to drill a penalty kick over from just a metre inside the visitors' half.
Early on the second-half, Chiefs failed to roll away at the ruck well inside their half in the 54th minute. It was a monster kick but Ford made it to take the score to 12-8 to Bath.
On the hour mark, Exeter were quick to take advantage of a loose ball in Bath's half, captain Dean Mumm kicking through and showing good pace to touch down in the right-hand corner. Steenson's conversion failed after bouncing off the upright, but Chiefs now led 12-13.
After 63 minutes, Exeter wheeled the scrum under enormous pressure from the Bath pack and were penalised. Ford, banged over the penalty to edge Bath 15-13 ahead.
The attacking momentum soon got Bath in a good position that allowed Ford to slot a drop goal. 18-13 to Bath.
Steenson got his team back to within two points after Bath were penalised at the scrum, and with the score now at 18-16, the tension at the Rec was palpable. Moments later, the Chiefs were given another penalty following a ruck infringement by Bath, but Steenson's effort was fractionally wide.
Bath were then awarded another penalty and Ford, having done so from a similar position almost 20 minutes earlier, kicked the crucial three points. 21-16.
With time up on the clock, Ford who booted the ball into touch to signal the end of the game.
Final Score: Bath Rugby 21 - Exeter Chiefs 16
What a super game of rugby, nothing beats a noisy Rec and a win for the mighty Bath!