Looking a far more fluent outfit than the side that stuttered through the first half of the season, they saw off the Irish challenge with two tries in the last five minutes, the last coming in the final play of the game from prop Anthony Perenise.
Replacement fly-half Tom Heathcote converted all four tries and also kicked two penalties. The other Bath scores were a Stephen Donald penalty, a penalty try and touchdowns by Nick Abendanon and Nathan Catt.
It was quite a comedown for the Exiles after their victory over Saracens last weekend but they were undermined by a penalty count of 18-5 - and three yellow cards.
The only bright moment was a thrilling breakaway try by replacement scrum-half Jack Moates, but the defeat leaves them back in the relegation dogfight.