Leinster's recent resurgence continued at the Sportsground as they fought their way to a fourth successive win in all competitions.
In what was a forgettable Magners League derby, Connacht missed out on a losing bonus point as Frank Murphy's pass was intercepted by young flanker Dominic Ryan for an injury-time try.
Winger Isa Nacewa grabbed a 14th-minute try for Leinster, who led 5-3 at the break. The visitors maintained their advantage, despite a second penalty from Ian Keatley, as Jonathan Sexton converted Ryan's effort to complete his eight-point haul.
Leinster dominated possession and territory for long stretches of this game, without hitting any heights in terms of performance and they just did enough in the end against a disappointing Connacht side.
There was a buzz of anticipation at the Galway venue when winger Fionn Carr got on the ball, but that was all too rare and Leinster's slick lineout staved off the early pressure.
The visitors used the set-piece to set up Nacewa's score. Scrum-half Isaac Boss blasted through a gap at the back of a lineout near halfway, and looped a long pass out to the left for Nacewa to gather and step past Darragh Fanning for well-executed try.
Sexton miscued the conversion but he was influential in open play, his inside pass putting flanker Sean O'Brien raiding through the middle.
Connacht's confidence was clearly dented by that try and they were kept on the defensive for most of the first half.
Leinster worked a maul in the 22 and almost created an opening for stand-in captain Jamie Heaslip on the left - but the covering Fanning and Ray Ofisa bundled him into touch.
Sexton's punt towards the right corner was gathered by the alert Gavin Duffy and Connacht soon lifted the siege.
A ruck offence from O'Brien allowed Keatley to claw back some territory and after a similar infringement from Cian Healy, he opened Connacht's account with a 34th minute penalty.
Keatley should have sent the hosts ahead but his poor miss from a late penalty, just to the right of the posts, summed up an up-and-down half from Connacht.
The westerners gave away some cheap penalties as the second half resumed, Sexton slotting a 49th minute opportunity from a left-sided position. It was just reward for his forwards, who led in the physicality stakes.
Sexton missed a drop goal attempt from near halfway, and the game was crying out for some continuity, with referee George Clancy's whistle peppering the night sky.
Connacht showed what they could do when, from their first visit of the half to Leinster's 22, they garnered a penalty which Keatley despatched from in front of the posts for 8-6.
Sexton replied in the 65th minute after good carries from Shane Horgan, replacement Gordon D'Arcy and man-of-the-match Richardt Strauss.
Leinster were knocking on the door for a clinching try, Carr doing well to halt a diagonal run from replacement Fergus McFadden.
With three minutes left, Sexton was narrowly wide with another drop goal shot. A Carr and Sean Cronin-inspired break, with the latter chasing his own kick up the left touchline, brought Connacht back to life.
A knock on and the lack of a reward for a huge shove in the scrum saw Connacht remain five points adrift and as they pushed for a late opening, Ryan snatched Murphy's pass on the Connacht's ten-metre line and sprinted clear for a sucker-punch score.