Connacht failed to turn a promising maul into a scoring chance and Leinster responded in decisive fashion, countering from deep with flair before Richardt Strauss' pass out of a tackle put Kearney over in the left corner.
But that was the end of the Welsh region's scoring for the afternoon at the Parc des Sports Aguilera, digging deep to produce a defensive performance that largely kept Biarritz at bay.
The six powerplay overs produced 65 runs for England and although Botha returned to briefly calm the scoring rate, he was frustrated when Kieswetter, on 29, lofted to deep mid-wicket where JP Duminy settled under the ball only to fumble the chance.