Resuming on 13-2 and trailing by 260, the hosts were dismissed for 221 in their second innings as Notts seamer Fergus O'Neill claimed 5-39.
Charlie Allison top scored for Essex with 56 off 104 balls before being trapped lbw by Liam Patterson-White, who took 3-66.
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Leicestershire claimed a first Division One win in 23 years by beating Yorkshire by an innings and 39 runs at Grace Road.
Yorkshire resumed on 32-2 in their second innings - trailing by 236 - and were all out for 229 following three wickets apiece for Josh Davey, Alex Green and Ajaz Patel.
Leicestershire, whose decisive first-innings total of 453 was underpinned by centuries from Rehan Ahmed and Nick Kelly, remain bottom of the table following promotion as Division Two champions.
Eddie Jack took four second-innings wickets as Hampshire secured a 118-run victory over second-placed Sussex at Hove.
After Hampshire increased their overnight lead to 252 by racking up 411, the hosts were skittled for 134 in their second innings, with Jack's exploits aided by three wickets each for Kyle Abbott and Felix Organ.
Somerset lead Warwickshire by 219 with four second-innings wickets in hand thanks to an unbeaten partnership of 193 between Thomas Rew (133no) and captain Craig Overton (89no).
Surrey lead Glamorgan by 145 runs with one second-innings wicket remaining following a century from captain Rory Burns (115) at Sophia Gardens.
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