Bath fly-half Chris Malone kicked a superb injury-time conversion to seal victory over Connacht at the Rec.
Winger David Bory scored in the corner to level the scores at 19-19 on 82 minutes, but Malone's kick snatched the points for the home side.
Newcastle were hammered 41-12 by Brive in a one-sided encounter in France.
Worcester lost 29-23 to Clermont Auvergne while Harlequins enjoyed a 57-10 win over Montpellier and Saracens beat Narbonne 37-20.
Quins made short work of the French side, with three tries in the final five minutes adding gloss to the scoreline and Mike Brown notching a hat-trick.
Meanwhile, Bucuresti full-back Florin Vlaicu kicked 12 points as his side completed a famous 32-27 victory over French club Bayonne.
And Montauban mauled Petrarca Rugby 53-5, with winger Sylvain Jonnet and hooker Tony Testa both bagging braces among their side's eight tries.