The holders had Ireland fly-half Jonathan Sexton's prolific boot to thank as he kicked all their points, and they held on despite 16-times capped international Banahan's late try giving Bath a one-point advantage after he received Jack Cuthbert's offload following a Francois Louw turnover.
But Sexton struck back to safeguard Leinster's unbeaten's Pool 3 record, who twice came from behind to forge ahead as Olly Barkley's conversion and two penalties went in vain for the now third-placed Bath.
Similarly, England's scrum-half Ben Youngs first-half try ultimately proved fruitless as Leicester Tigers relinquished their Pool 4 undefeated streak in a 30-12 reversal to Clermont Auvergne at the vociferous Stade Marcel Michelin.
Clermont recorder their 35th straight home win, but fly-half Brock James saw his grubber kick charged down as Ben Youngs capitalised from a Toby Flood fly-hack to crash over in the corner for an early 5-3 lead.
Two-time European champions Leicester saw 20-year-old England centre Manu Tuilagi and George Chuter sin-binned as Wesley Fofana, who did his own hopes of selection no harm for Philippe Saint Andre's new squad, twice touched down as the French side eventually outclassed and sent Richard Cockerill's troops to third in the group.
In Sunday's only other Heineken Cup fixture, Scotland fly-half Ruaridh Jackson scored a penalty as Glasgow Warriors secured their second win in Pool Three with a 20-15 downing of Montpellier at Firhill.
David Weir's four penalties and a try from Argentinean Federico Aramburu steered the Scottish club to victory, despite crossovers from Eric Escande and Sakiusa Matadigo and kicks from Bustos Moyano.