Prop Vakh Abdaladze marked his first match in a year and a half after a back injury with a try at the Sportsground but it was not enough to secure victory in an entertaining clash.
The 25-year Georgian native, who made his 11th appearance for Leinster when he last played against Zebre in October 2019, did well on his return in a game Connacht won by six tries to five.
Connacht, with Conor Fitzgerald dictating matters at out-half and Abraham Papali’i using all his bulk to great impact on the crash ball, led 26-10 at the break against a Leinster side guilty of poor handling.
Scrum-half Colm Reilly, Papali’i , Australian Ben O’Donnell and centre Diarmuid Kilgallen crossed for the Connacht tries with the wind at their backs.
Winger Rob Russell got Leinster’s first try and Abdaladze crashed over after a tapped penalty after 18 minutes, with hooker Dan Sheehan getting their third just after the restart and replacement prop Jack Boyle crossed shortly after coming on for the first of two tries.
In between impressive Connacht lock Cian Prendergast finished after several drives and former All-Ireland minor hurling winner Shane Jennings got their sixth.