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Eight group matches were played on Sunday, with Worcestershire clinching a dramatic four-run victory in the final over against Hampshire.
But Middlesex again caught the eye with another dominant performance, dismissing Glamorgan for just 66 and then requiring only 9.1 overs to reach their victory target.
Middlesex are the only side to have won their first three matches, while Worcestershire are one of three teams to have won two out of two.
Elsewhere, former England Test batters Keaton Jennings and Tom Westley struck centuries in wins for Lancashire and Essex respectively, while Ben Coad claimed a maiden five-wicket haul in white-ball cricket as Yorkshire thrashed Sussex.
One-Day Cup results, scorecards and fixtures
Group A: Lancashire claim first win Leicestershire's winning start came to an end in a high-scoring meeting with Lancashire at Grace Road.
Jennings starred with 135 off 134 balls as the visitors posted 383-4 and, in reply, the Foxes were reduced to 22-4 before a 179-run fifth-wicket partnership between Hamza Shaikh (91) and Ruan de Swardt (126) brought the hosts back into contention.
Despite the Foxes taking the match into the final over, Lancashire held on for their first win by a 21-run margin.
Cameron Bancroft (89 not out) and James Bracey (83) scored half-centuries as Gloucestershire also claimed their first victory of the campaign with a six-wicket win over Kent in Bristol.
The hosts' success owed much to a strong performance in the field as seamers Will Williams and Luke Charlesworth returned figures of 3-33 and 3-42 respectively to help dismiss Kent for 208.
Warwickshire are now the only Group A side yet to register a victory in this year's competition after a comprehensive 125-run defeat by Somerset at Taunton.
Somerset captain Lewis Goldsworthy (103) led from the front with his third List A century as last year's beaten semi-finalists scored 337-8.
In reply, Warwickshire were bowled out for 212, with 19-year-old seamer James Theedom claiming 4-54 in what was only his third List A appearance.
Elsewhere in Group A, Surrey eased to a six-wicket win over T20 Blast winners Northamptonshire Steelbacks in Guildford.
Benji Floros took 4-60 as the Steelbacks ended on 254-8, but Surrey had little trouble chasing their target, with Adam Thomas ending on 83 not out as they won with almost seven overs to spare.
Worcestershire appeared to be cruising towards victory when Hampshire, chasing 308, needed 48 runs to win with 21 balls remaining and one wicket in hand.
Some big hitting from Andrew Neal took Hampshire to the brink of an astonishing success but, requiring five more off the final three balls, he edged spinner Fateh Singh behind to fall for 48 off 22 balls.
The late drama at New Road was in sharp contrast to events earlier in the day at Radlett, where Middlesex made short work of Glamorgan's batting line-up.
Naavya Sharma (4-29), Toby Roland-Jones (3-35) and Noah Cornwell (3-1) were the only three bowlers used as Glamorgan, who were 44-1, lost their final nine wickets for 22 runs.
Josh de Caires hit 10 fours in his 45 not out as the hosts completed victory within three hours of the match starting.
At Hove, an early rain shower meant a slightly reduced match of 48 overs per side.
Opener Will Luxton made 117 in Yorkshire's 325-7 and Coad's four wickets with the new ball left Sussex on 21-5 as they chased a revised target of 325.
Coad ended with 5-12 from seven overs as Sussex were bowled out for 140 to lose by 184 runs on the Duckworth-Lewis (DLS) method.
Essex beat Derbyshire by nine runs at Chelmsford in the other match in Group B, with both captains leading their sides' respective batting causes.
Westley, making his 500th career appearance in all formats, scored 102 off 97 balls in the hosts' 257-7.
Harry Came (97) shared an opening stand of 113 with Martin Andersson but the match looked in the balance when Derbyshire needed 100 more with five wickets in hand.
Charlie Bennett (3-32) broke a seventh-wicket partnership worth 45 between Ross Whiteley and Nick Potts, which proved crucial.
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