Glasgow set up Leinster tie
In what was their last ever game at Firhill Stadium before their summer move to the recently redeveloped Scotstoun Stadium, the Warriors impressed throughout and grabbed the spoils thanks to tries from DTH van der Merwe and John Barclay.
The rest of the points came from the boot of Duncan Weir, while replacement Ruaridh Jackson also chipped in with a late conversion. Despite their loss, Connacht remained in eighth place in the table, their highest league finish ever.
Edinburgh recorded only their sixth win of the season and sent Scotland's most-capped player Chris Paterson into retirement on a winning note when they saw off Benetton Treviso 44-21 with a convincing performance.
The home side had tries from Dave Denton, Greig Laidlaw, Paterson, Tim Visser and Kyle Traynor, plus a 19-point contribution with the boot from Laidlaw.
The visitors had a touchdown double by Ludovico Nitoglia and one from Edoardo Gori, all three of them converted by Kris Burton.
Having failed to reproduce their sparkling European form in league competition, the hosts were already consigned to second-bottom place in the table, and their only incentive was to give Paterson a winning send-off.
Glasgow's win over Connacht denied the Scarlets their place in the top four, but they did everything they could to ensure Jones and the others who are leaving the region enjoyed a fitting farewell to Parc y Scarlets,
A fabulous contest was in the balance was in the balance until the final minutes when the Scarlets claimed a penalty try, with the Blues playing their part with some superb rugby of their own. Double British Lion Jones will now head to Wasps, 16 years after making his debut for Llanelli.