Leinster march on Europe in the knowledge that they failed to make a dent in Connacht's defences, with the reigning Magners League champions succumbing to a shock 19-18 defeat in Galway on Sunday.
Ian Keatley came back to haunt his old province by kicking four penalties and converting Mike McCarthy's lone try to inspire Connacht to their first win over Irish opposition since December 2005.
With McCarthy having been controversially red-carded straight after his 44th-minute score, Michael Bradley's men required a real backs-to-the-wall effort to hold on to their lead.
But, after weathering a storm in which Leinster fluffed numerous try-scoring chances, the hosts' seven-man pack wound down the clock with a superb spell of possession rugby.
Wanting to bounce back from last week's reversal to Munster, Leinster threatened twice in the opening five minutes through Rob Kearney and Luke Fitzgerald.
And while Felipe Contepomi, making his 100th appearance for the visitors, did boot his side into a 9-3 lead, Connacht were making a game of the provincial derby.
Contepomi, recovering from his kicking nightmare against Munster, cancelled out a Keatley strike to move Leinster 6-3 ahead in the 26th minute, before Connacht second row McCarthy was rather harshly sin-binned.
Referee George Clancy adjudged that the former England Under-21 international had brought down a line-out and Contepomi landed the resulting kick for 9-3.
But Connacht, with Johnny O'Connor impressing in front of the watching Ireland head coach Declan Kidney, battled back to 9-9 while still down a man - key man Keatley converted two more penalties before the break.
Five minutes into the second half, the westerners conjured up a bit of magic for only their third try of the campaign.
O'Connor tore out of his half to begin a move in which Frank Murphy was involved twice.
Keatley then drew his man and put hooker Sean Cronin charging through before his one-handed offload sent McCarthy under the posts.
But a dust-up ensued after the try. McCarthy was spotted leading with his head on Rocky Elsom and the Australian retaliated with a punch. Both players received yellow cards, meaning the try-scorer's night was over.
Keatley converted and crucially managed to trade penalties with Contepomi while both sides were down to 14 men.
Leinster shunned an immediate shot at the posts as, with Elsom back, they pressed for a pushover try.
Connacht were in no mood to give in, however, and although Contepomi landed a further brace of penalties, a try eluded them.
Fitzgerald, Elsom and Cian Healy each failed to convert when in sight of the whitewash and after Jonathan Sexton pushed a drop goal shot wide, Connacht held on for a victory which moves them off the foot of the table.
Pen: Keatley 4
Pens: Contepomi 6
Yellow cards: McCarthy (Connacht) - 29, 46, Elsom (Leinster) - 46.
Red cards: McCarthy (Connacht) - 46
Connacht: 15 Fionn Carr, 14 Liam Bibo, 13 Gavin Duffy, 12 Keith Matthews, 11 Michael Roberts, 10 Ian Keatley, 9 Frank Murphy, 8 Colm Rigney, 7 Jonny O'Connor, 6 John Muldoon (c), 5 Adrian Farley, 4 Michael McCarthy, 3 Ronan Loughney, 2 Sean Cronin, 1 Brett Wilkinson.
Replacements: 16 Conor Muldoon, 17 Robbie Morris, 18 Andrew Browne, 19 Michael Swift, 20 Kieran Campbell, 21 Troy Nathan, 22 John Hearty.
Leinster: 15 Rob Kearney, 14 Shane Horgan, 13 Luke Fitzgerald, 12 Felipe Contepomi, 11 Simon Keogh, 10 Jonathan Sexton, 9 Chris Keane, 8 Stephen Keogh, 7 Sean O'Brien, 6 Rocky Elsom, 5 Devin Toner, 4 Leo Cullen (c), 3 CJ Van Der Linde, 2 John Fogarty, 1 Stan Wright.
Replacements: 16 Cian Healy, 17 Brian Blaney, 18 Trevor Hogan, 19 Cameron Jowitt, 20 Chris Whitaker, 21 Fergus McFadden, 22 Gary Brown.
Referee: George Clancy (Ireland)
Touch judges: Peter Fitzgibbon (Ireland), John Lacey (Ireland)
Television match official: Dermot Moloney (Ireland)