There were also wins for Hampshire, Derbyshire, Gloucestershire, Somerset and the defending champions, Leicestershire, to follow those completed by Lancashire, Kent and Worcestershire on Friday.
Saqlain, the Surrey spinner, returned 7 for 38 to give him match figures of 12 for 110 as Durham were all out for 139 midway through the penultimate session, chasing an improbable target of 366.
A last-wicket stand of 56 by the Yorkshire pairing of Richard Harden (69) and Ryan Sidebottom (26no) forced Leicestershire to bat again - but only for eight balls after they were set a victory target of just seven at Grace Road.
Shaun Udal claimed three morning wickets for a total of 6 for 47 as Hampshire dismissed Glamorgan for 177 to win by an innings and six runs before lunch on the final day at Swansea.
Glamorgan resumed on 102 for 6 and only a late 57-run stand by Dean Cosker and Darren Thomas prolonged the inevitable outcome.
Derbyshire also wrapped up victory before lunch, reaching a target of 66 for the loss of only Michael Slater to beat Middlesex by nine wickets with two sessions to spare at Lord's.
Gloucestershire completed a routine seven-wicket victory over Nottinghamshire as Jack Russell (46) and Rob Cunliffe (45) pointed them towards their target of 154 with a session to spare at Bristol.
Somerset lost both openers but had few problems knocking off the 94 runs they needed to win by eight wickets having rushed out the last four Sussex batsmen for the addition of 49 at Taunton.Reuse content