Connacht dominated proceedings in the first half and were worthy of their 22-6 half-time lead as David McSharry, Fetu'u Vainikolo and Tiernan O'Halloran all went over for the Galway side.
The second half was more even as Leinster showed some resolve but two late tries from forwards George Naoupu and Ronan Loughney put some gloss on the scoreline.
Ian Madigan put Leinster into an early 3-0 lead with a penalty although Connacht thought they had scored the first try of the match when Michael Swift bulldozed over on his 150th appearance for the club only to have the television match official rule it wasn't grounded.
But they did score minutes later when a fantastic line run from McSharry saw him fly over the line and send the home support into raptures with just 13 minutes on the clock although Madigan quickly closed the gap with another penalty.
Connacht were rewarded for their impressive start on 23 minutes when Vainikolo burst down the right-hand side and side-stepped John Cooney expertly to make the score 14-6 after Parks added the extras.
And Leinster's half got worse when Brendan Macken was yellow carded and Connacht added eight points through an O'Halloran try and a penalty from Miah Nikora to finish the half superbly.
Leinster started the second half in better fashion but no side was giving any quarter as Connacht attempted to increase their lead through some speculative drop goals.
But Connacht looked to have wrapped up a surprise win over the Irish province when Naoupu bundled over to make it 27-6 with just six minutes left on the clock.
And a miserable night for Leinster was rounded off in the final two minutes when substitute prop Loughney also joined in the party to score a try and round off a wonderful evening for Connacht.
|Connacht Rugby Score Card|
|Leinster Rugby Score Card|