A drop-goal in the last minute of normal time by Chris Malone earned Bath the narrowest of victories in front of a record Zurich Premiership crowd of 22,840 at the Madejski Stadium.
The league leaders, shorn of eight international players behind the scrum, extended their lead over second-placed Wasps to six points.
Irish thought they had snatched victory in the ninth minute of injury time but Barry Everitt's drop-goal attempt fell just wide of the post.
Bath's success was due entirely to their pack, which fashioned two tries from driving mauls in each half.
The roof was raised after nine minutes when right wing Paul Sackey profited from sloppy lineout play by Bath to claim the first try.
Bath hooker Jonathan Humphreys threw too long, Kieron Dawson drove deep into the Bath 22 and quick transfer of the ball gave Sackey the glimpse of the line he needed.
But when Irish scrum-half Darren Edwards was first to see the yellow card as referee Tony Spreadbury sent him to the sin-bin on 23 minutes for kicking an opponent. Australian Malone kicked the goal.
On the half hour Bath opted to take a lineout from a penalty in the Irish 22. The visiting forwards driving prop Duncan Bell over for the unconverted try.
Mapletoft responded to bring the scores level and edged Irish ahead after Bath scrum-half Martyn Wood was sent to the sin-bin on 37 minutes for obstruction.
Malone responded with a 50-metre kick from the touchline on the stroke of half-time and the exchange of penalties continued after the break when Mapletoft goaled from 45 metres.
But the Bath forwards sent substitute hooker Lee Mears over Malone converted.
Irish's replacement fly-half Everitt punished a loose-play infringement with a penalty from in front of the posts.
But Malone grabbed his chance on 79 minutes to open up a 21-17 lead and although Everitt added another three points deep into injury time the clock ran out.
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