Middlesex 289 for 5 (Gubbins 92, Robson 79) beat Glamorgan 285 (Hemphrey 87) by five wickets
The Middlesex pair, whose efforts underpinned their side's win against Somerset earlier in the week, led the way again with innings of 92 and 79 respectively to secure victory against the Welshmen at Lord's.
Gubbins' knock was his fourth half-century of the tournament - although he has also passed 90 in three of those - and lifted Middlesex to second place in the South Group table.
Glamorgan, who are now out of contention, posted 285 from 49.4 overs after being put in to bat, centred around Charlie Hemphrey's slick 87 - his highest List A score.
Middlesex made an early breakthrough when David Lloyd, having hit Toby Roland-Jones for two boundaries, attempted another and was caught by Nathan Sowter at backward point.
But Jeremy Lawlor (38) and Chris Cooke (46) kept the scoreboard ticking over during the powerplay with a glut of attacking strokes as they added 71 for the second wicket.
Leg-spinner Sowter, who has consistently made an immediate impact in this tournament, continued that habit by persuading Lawlor to drive at his third delivery and edge it behind.
However, the introduction of Robson (1 for 27) - who had never previously sent down a ball in white-ball cricket - pegged Glamorgan back, with Marnus Labuschagne (16) chopping his third delivery onto the stumps.
Cooke perished in the next over, prodding Roland-Jones (3 for 46) to mid-wicket as the visitors slumped to 116 for 4, but Hemphrey and Billy Root (37) rebuilt their innings with a fifth-wicket stand of 80.
Sowter (4 for 58) struck back with two wickets in as many deliveries, deceiving Root with a slower ball and snapping up the return catch before having Dan Douthwaite stumped for a duck.
But Hemphrey maintained his side's momentum, striking the ball cleanly as he clobbered 14 off one Tom Helm over before he eventually became the ninth man to depart, holing out to Robson at deep extra cover.
The target of 286 looked a long way off when Middlesex lost Max Holden (0) in the second over of their reply, flashing at a wide ball from Marchant de Lange.
It took the home side until the sixth over to register a boundary, when Gubbins hooked de Lange for successive fours and that served to lift the shackles.
Robson, fresh from his maiden white-ball century, began to increase the tempo, flicking Timm van der Gugten into the Mound Stand for six as he outscored his partner.
The pair added 147 for the second wicket - only for Robson's hopes of a second successive ton to be dashed when he charged Root (2-36) and was stumped for 79.
Cooke's third dismissal arrived in the next over, when Ross Taylor (2) edged Labuschagne behind to leave Middlesex uncertainly positioned at 152 for 3.
Gubbins seemed set to finally pass three figures, sharing a partnership of 64 with Stevie Eskinazi, but he had reached 92 from 91 balls when he clipped Root to mid-wicket, with 70 still required.
However, Eskinazi survived an early life - when his miscued pull dropped between three fielders - to steady the ship with an unbeaten 71 off 58 deliveries and clinch victory with 15 balls to spare.