Middlesex lost their last six second-innings wickets for the addition of 82 on the final morning to be dismissed for 219. Adil Rashid finished with five for 78.
That narrowly avoided the ignominy of an innings defeat but Yorkshire claimed the five runs they needed in the fourth over of their chase.
Durham and Warwickshire were set for a potentially tight finish at Chester-le-Street after the visitors were set a target of 267.
Michael Richardson took his overnight 26 to 55 as Durham added another 46 to their second-innings total before being bowled out for 198 on the third morning.
Graham Onions struck twice as Warwickshire slipped to 47 for two after starting their pursuit before lunch.
Derbyshire posted 391 against Nottinghamshire at Trent Bridge. Contributions from Richard Johnson (22), David Wainwright (22), Mark Turner (23 not out) and Mark Footitt (24) saw the visitors' last four wickets add 85.
Nottinghamshire were 13 without loss at the interval. At Arundel, Surrey moved on to 102 for two in their reply to Sussex's first-innings 295.
Arun Harinath (23) and Rory Burns (36) were the men out at the interval with Vikram Solanki (26 not out) and Ricky Ponting (six not out) at the crease.
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