The Australian 'king of spin' was instrumental in restricting Essex to a total of 153 all out off 43.1 overs in reply to the hosts' 184 for seven.
Earlier, wicketkeeper-batsman Nic Pothas (64) contributed a half-century at the top of the order - and Will Kendall (55 no) added one lower down - as Hampshire grafted their way to what proved a winning total.
Matthew Elliott led Glamorgan to an eight-wicket victory over Limited Overs specialists' Gloucestershire at Bristol.
The Victoria left-hander shared an opening stand of 98 with Robert Croft (56) and finished with an unbeaten 91 as the Welshmen bettered a target of 213 for eight with almost eight overs to spare.
The Gladiators' total had been built on a tenacious 79 from Matt Windows.
Lancashire had to dig deep against Kent to edge home by three wickets in the closest finish of the day, at Old Trafford.
Openers Mal Loye and Iain Sutcliffe gave Lancs a handy start with a 93-run stand in pursuit of 203 all out.
But they had to bat right down the order to prevail by three wickets as number eight Kyle Hogg chipped in with a vital 37 not out to finish the job with only four balls remaining.
Lancashire's England hopeful Sajid Mahmood had earlier taken three for 39 to help restrict Kent, despite some handy tailend batting from Rob Ferley and James Tredwell which could not stop the visitors being bowled out just one over short of their entitlement.
In Division Two, Russell Warren (81) and David Hussey (87 no) led the way as Nottinghamshire inflicted a heavy defeat on Yorkshire at Trent Bridge.
The pair shared a 106-run fourth-wicket stand in a total of 291 for six, after the hosts had chosen to bat first.
Yorkshire were never in the hunt in reply, with only captain Craig White (59) and Australian Ian Harvey briefly getting going in a total of 187 all out in only 34.4 overs. Notts shared the wickets out fairly - Mark Ealham and Stuart MacGill the greediest with three each.