Cameron Bancroft produced his best Vitality Blast performance with a knock of 87 from 54 balls as Gloucestershire kept Middlesex at bay and kept their hopes of a quarter-final place alive.
The former Australian Test batsman shared an opening partnership of 65 off 42 balls with Miles Hammond to lay the foundation for the visitors' score of 8-179 in Chelmsford.
Despite a brave, unbeaten 73 off 52 by Middlesex captain Leus du Plooy, his side lost six wickets for 39 and failed to reach 169 for seven.
Matt Taylor took 2-17 for Gloucestershire, but the team will go home empty-handed unless Essex loses its final game against Hampshire on Friday.
Bancroft, who also plays for Western Australia and Big Bash team Sydney Thunder, was soon on his feet for Gloucestershire, taking six runs off Tom Helm and then hitting two more boundaries off Noah Cornwell.
He and Hammond passed 50 at the start of the sixth over before Luke Hollman made the breakthrough when the left-hander missed a point.
Bancroft reached his half-century in style after 31 balls, inflicting two consecutive sixes on Hollman, but the wickets continued to fall until Ben Charlesworth joined him at 4-105.
The pair scored 46 off 29 before Blake Cullen had Charlesworth caught at point and Ryan Higgins struck twice in an over, with Bancroft out to long-on and Ollie Price run out.
Higgins finished with 2-25 from his four overs and Gloucestershire narrowly missed the total of over 180.
Andersson had fun against Shaw, scoring 14 from the first three balls of his over.
Du Plooy made his half-century from 32 balls with a powerful straight six against Tom Smith – but Andersson narrowly missed it as he was caught by Hammond.
Max Holden then miscued and the ball went into the backward point position and Higgins was denied by a ball from Price before Jack Davies and Joe Cracknell were both caught at deep.
Despite some late hits from Josh de Caires and Helm, Payne finished the game with a score of 1-26.