An unbeaten 50 from wicket-keeper John Simpson scuppered Unicorns' hopes of a famous win as Middlesex claimed a one-wicket victory in their Yorkshire Bank 40 clash at Lord's.
Simpson kept a cool head as the hosts overall Unicorns' total of 208-7 with five balls and a single wicket to spare.
The defeat was cruel on the Unicorns, who put in a spirited display with bat and ball only to stay bottom of Group C and without a win.
In pursuit of 209 for a fifth win in nine starts, Middlesex lost Dawid Malan (eight) to a good tumbling catch by keeper Lewis Hill, but re-grouped with a second-wicket stand of 65 between Paul Stirling and Joe Denly.
Josh Poysden had Stirling stumped for 42 and enjoyed further success in pegging back Eoin Morgan's off stump and then in trapping Gareth Berg (16) lbw to finish with figures of 3-33.
Luke Beaven had Neil Dexter (4) caught at deep cover off a miscued back-foot force, but Denly moved to a 63-ball 50 before he too fell to Beaven, bowled when working across the line to leg to make it 140-6.
With nerves jangling, Ollie Rayner (9) aimed to push drive at a Chris Skidmore away swinger to be caught behind, then Toby Roland-Jones went back in defence to his first ball to go leg before to Beaven, who finished with 3-43.
With Middlesex still needing 24, Skidmore found the outside edge of James Harris's bat and Hill pulled off a stunning catch to remove him for two, but Simpson (50 not out) managed to complete the narrow win.
Unicorns had earlier lost opener Matt Lineker for 11 before Tom Lancefield clattered five fours in a cameo 28, with Michal O'Shea making a more circumspect nine.
The frenetic nature of the Unicorns innings continued through Hill, who clubbed 31 from 29 balls including four fours, before driving off-spinner Stirling flew into the hands of Berg at extra cover.
Garry Park (43) and former Somerset stalwart Keith Parsons (64no) combined for a fifth wicket stand of 77 in 13 overs before the former fell to Toby Roland-Jones (3-33).
Beaven (1) was caught in the deep off Harris in the 38th over but 40-year-old veteran Parsons finished as unbeaten top-scorer.