The celebrations were put on hold by second-placed Lancashire, who need to win against Somerset but staved off defeat until Friday.
Lancashire led by 45 at Thursday's close with only two wickets left.
They had earlier been forced to follow-on after slumping to 133 all out in reply to relegation-threatened Somerset's first innings haul of 335.
Essex, promoted last year and now heading for a first title since 1992, declared with a first innings total of 369 for nine after Warwickshire had laboured to 201 all out.
Varun Chopra (98), Dan Lawrence (78) and James Foster (68) all scored half centuries as the still-unbeaten visitors built up a first innings lead of 168.
Warwickshire reached 55-5 at an early lunch, with the covers coming on under dark skies and the threat of rain, but a catch off Henry Brookes gave Simon Harmer his fourth wicket of the second innings and sealed the victory.
"The last challenge is to go unbeaten this season but we're going to celebrate first," Essex captain Ryan ten Doeschate of the Netherlands told the BBC.
"I know it's not confirmed but I think whatever Lancashire do now is pretty irrelevant."
(Reporting by Alan Baldwin, editing by Christian Radnedge)
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