Frost resumed on 121 and took his score first past the 150 mark, then made 200 before having to end his innings on 242 when Darren Maddy declared on 514-9, some 173 runs ahead of Essex's first innings total.
Frost's innings lasted 466 balls and contained 30 fours and one six. Rikki Clarke, chipped in with 41 and there were 47 extras.
It was a decision that came at the right time as Warwicks need to get a win from this game in order to have a chance of promotion back to the top flight.
Chris Woakes struck early getting Gallian LBW for a duck and the score at the close was 125-1 after 28 overs.