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Bath produced a fantastic late rearguard performance to hold out for a 22-19 victory at Leinster.
The match was a tight affair throughout the 80 minutes, with both sides scoring a try apiece through Felipe Contepomi and man-of-the-match Andy Beattie.
However, Bath stole into a six-point advantage in the second half, and despite Leinster's mammoth efforts, they could not find a way back.
The home side starting positively, pinning Bath back through a fine kick from Girvan Dempsey, and Contepomi was able to knock over a cool drop goal from the next play.
Four minutes later, the Irishmen should have scored their first try of the contest. French winger David Bory failed to deal with an awkward bounce, and from the resulting turnover scrum half Brian O'Riordan dashed for the line, but he was held up by two Bath defenders.
However, Leinster were not made to wait long to appease for that missed opportunity, as Contepomi scored a well-worked effort. After good ball from the scrum, the fly half went on a simple loop to avoid the Bath tacklers and cross for an easy score.
Bath replied with two Olly Barkley penalties for 13-6, and should have had a further three-pointer but for some ridiculous back-chatting from Martyn Wood, which cost his side a simple penalty opportunity.
The visitors' game plan appeared to be focused on building the phases and drawing penalties from their opposition, and they did manage to move within four points ahead of the interval - setting up an intriguing second 40 minutes.
Bath continued their powerful work directly from the restart, and after a super surge from Danny Grewcock, they forced David Blaney to cynically bring the play to a halt - resulting in a yellow card for the hooker.
And with Leinster minds elsewhere, Barkley took a clever quick tap from the penalty before chipping the ball wide to Beattie, who pounced on the fortunate bounce to make it 16-13 in the visitors' favour.
However, much like Gloucester did against Bath last week, John Connolly's side failed to capitalise on their extra man, and it was Leinster who took charge of the game with some excellent ball handling.
A Contepomi penalty restored parity to the scores, and Bath struggled to get their hands on the ball as the 10-minute absence of Blaney ticked away.
The Leinster attack steadily increased and Ireland international Gordon D'Arcy was the length of Frikkie Welsh's fingertips away from setting up a score for his side.
The talented centre broke through the Bath rearguard before attempting to feed the ball out to Dempsey, but Welsh was alert to the danger and made a try-saving interception.
And how crucial that hand proved to be.
Led forward by the exemplary Beattie, Bath moved into a six-point lead with 15 minutes left, courtesy of a penalty from Barkley and then a thunderous drop goal from Chris Malone.
Contepomi responded once again to narrow the deficit to three and set up a highly tense finale inside the RDS.
Backed by the roar of the home crowd, Leinster summoned one last effort and they surged towards the Bath line, but the visitors' defence held firm for a terrific victory.
Leinster: (13) 19
Pens: Contepomi 3
Bath: (9) 22
Pens: Barkley 4
Read the thoughts and opinions of Stuart Barnes with skysports.com