A try seven minutes from time by replacement lock Dave Hansbury proved crucial as Connacht beat Leinster 20-14 at Donnybrook for their second win of the championship.
The impressive Paddy Pearson converted a penalty on 15 minutes to put the visitors ahead and he set up Rory O'Connor for the first of his two first-half tries two minutes later.
Trailing 15-0 at the break, Leinster responded with a try from Dave Murphy, which Bryan Croke converted.
Connacht were on the back foot for a while after that, but Hansbury's try gave them vital breathing space before replacement Ben Swindlehurst got in for an injury-time consolation.
Munster slipped out of contention with their second defeat when they were beaten 26-24 by Ulster.
Ulster started strongly at Limavady and were 14 points in front in as many minutes after Ryan Wilson and Stephen Robinson scored tries for Johnny Steenson to convert. Munster reduced the arrears with a Dara Meade penalty and a Dermot O'Sullivan try before Andy Kennedy crossed for Ulster to make the interval score 19-10.
Five minutes into the second period and Ulster increased their lead when scrum-half Matt Wright touched down for a converted try. Munster took advantage of a sin-binning with two Brian O'Sullivan converted tries.