Leinster, who have subsequently boosted thier Celtic Cup chances, held off a late rally from their fellow provincial opponents that saw tries from Matt Lacey and Bernard Jackman tries bring Connacht to within five points.
In the end Declan Kidney’s side, stripped of 14 players due to injuries and a combination of Six Nations and Rugby World Cup Sevens selection, proved strong enough to hold on for the win even when lock Des Dillon was sin-binned.
New Zealander David Holwell, who confirmed this week he will be returning home at the end of the season, was the saviour, slotting four penalties and a conversion.
Another foreign star, Argentine Felipe Contepomi provided a key intercept try on the half-hour after robbing the ball from Connacht veteran Eric Elwood on his own 22.
With the wind at their backs, Leinster slotted two penalties in the opening minutes with fit-again Ireland flanker Keith Gleeson – making his first league start since November 2003 – leading by example.
Elwood, pulled three back for Connacht and could have orchestrated a try if support had been quicker in coming when he broke the Leinster line midway through the half.
Leinster opportunistic try and conversion extended their lead and Holwell added another penalty in first-half injury time.
Connacht rallied after the break and McHugh grabbed another three-pointer, but their hard work was undone when Victor Costello struck off the base of a close-in scrum for Leinster´s second converted try on 53 minutes.
Connacht flanker Lacey powered over in the left corner on the hour-mark and Elwood converted his second score, a close range drive on 78 minutes but it was too late for Michael Bradley´s side as they remain without a home win in the league since November.
Final Score: Connacht 21 (Lacey, Jackman try, Elwood conv, 2 pens, McHugh pen), Leinster 26 (Contepomi, Costsello try, Holwell 2 conv, 4 pens)