Pat Lam's side were 16-11 victors over Dragons at the Sportsgrounds last evening.
Despite a second-half fight-back, Leinster lost to Glasgow, with a last-gasp Stuart Hogg penalty the deciding score.
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Captain Sean O'Brien was bitterly disappointed with his team-mates' display.
While Ulster came from 32-18 down to draw 32-apiece with Scarlets.
There's one game this afternoon, with Zebre playing host to Cardiff Blues.
