Sussex battled hard to keep the run rate up to give themselves a chance of making their 222-run target, led by Luke Wright with 91, but Kyle Abbot claimed figures of 5-14 to ensure that the hosts could not match Middlesex's total.
Yorkshire still needed 22 with just seven balls remaining after Keaton Jennings had ripped through the middle order, but Tim Bresnan and Adil Rashid fell just short as they went for broke off the last over.
Birmingham Bears needed four runs off the final ball to secure a closely-fought win over Northamptonshire, leaving their opponents still looking for their first win of the season.
Richard Levi hit a half-century to get the home side off to a bright start, but Josh Cobb was the only other batsman to reach 20 for Northamptonshire.
Muhammad Azharullah gave the side a chance, taking three wickets in quick succession to limit Birmingham's reply, but Will Porterfield helped the defending champions draw the scores level in the final over.
Porterfield was on strike for the final ball, but byes from Azharullah's delivery handed the Bears the last-gasp win.
The captain led the home side to a score of 193 off their 20 overs before Moises Henriques and Kumar Sangakkara got Surrey off to a strong start in their reply, but neither remained at the crease long enough to complete the chase.
Only Grant Elliott managed more than 30 for the visitors, allowing Daryl Mitchell to lead the Worcestershire run chase with 58, before Ross Whiteley hit the winning runs with almost three overs to spare.
Glamorgan fell short in their quest for a second win of the season as they were well beaten by Hampshire.
After winning the toss and choosing to bowl first, Glamorgan restricted their opponents to 148, led by Sean Ervine with 49.
Kyle Hogg and Michael Hogan led the attack, each claiming four wickets for the home side, but the top-order batsmen fell short as Glamorgan were quickly reduced to 13-3 in their reply.
Somerset picked up their first win of the season though, edging out Essex Eagles after surviving a run out appeal on the final ball of the match.