Kent 207 and 4 for 1 trail Essex 458 for 8 dec (Critchley 117, A Cook 87, Harmer 83*) by 247 runs
The 26-year-old faced just 168 balls in rattling up 117 runs as Essex put Kent to the sword while building a first-innings lead of 251. Critchley entered at 158 for 3 and departed 64 overs later on 408 for 7 when he picked out long leg to give part-time spinner Jack Leaning a rare wicket.
Alastair Cook had laid the foundations with a 176-ball 87, but some lusty late six-hitting by Critchley, Harmer and Doug Bracewell gilded the lily as Essex declared on 458 for 8. Hamid Qadri bore the brunt with figures of 3 for 120, while the Indian international Arshdeep Singh returned best Championship analysis of 3 for 58.
And to cap Essex's day, Twanda Muyeye departed to the last ball of the five overs left for Kent to see out when he went lbw pushing forward to Sam Cook for nought. Kent finished on 4 for 1.
But the real drama of the day came before play with the news that Nick Browne had retired hurt after feeling groggy overnight and failing an off-field concussion test. The left-handed opener was hit on the head by a short ball from Arshdeep in the evening session but batted on for a further two-and-a-half overs before being visibly ill after the penultimate delivery of the day. He then passed an on-field check and saw out the over.
Robin Das, who had originally stood in as the nominated substitute while Dan Lawrence made his way back from Old Trafford where he was stood down by England, then became Browne's replacement.
Das lasted five balls before he became another entry in the scorebook that needed an asterisk: the concussion substitute was caught by the substitute wicketkeeper Harry Finch, standing in for Jordan Cox who further depleted Kent's resources with a thigh injury.
Having put on 117 for the first wicket, thanks to the efforts of three men - but mainly Cook - Essex lost another almost immediately when Tom Westley was trapped lbw to give Arshdeep a second wicket.
Cook had looked in sparkling form the night before, stroking a dozen boundaries in his 64. But he batted for a further hour-and-a-half in the morning session, adding just 23 runs from 70 balls before looking a little disconsolate at being judged lbw to former Essex seamer Matt Quinn.
Lawrence, having made the journey down from Manchester, played an entertaining cameo of 25 that included an effortless six over midwicket before he attempted to sweep Qadri in a similar direction only to become a third lbw victim.
Critchley hammered Qadri over long-leg for the six that took Essex beyond Kent's first-innings 207 with only four wickets down, though it had taken them 17 overs longer. However, Walter's 90-ball 45 was ended by the third delivery with the new ball as he played down the wrong line to Arshdeep.
Rossington twice straight-drove Joey Evison for fours in a bright partnership with Critchley before he was deceived by Qadri's flight and turned to see his stumps disturbed.
Once Harmer had got off the mark to his 28th ball, he cut loose and needed just another 51 balls for his half-century, reached with a huge six off Qadri. But it was Critchley who caught the eye with some breathtaking, but orthodox hitting, and reach three-figures from 161 balls by pulling Quinn through midwicket for his 14th boundary that included two maximums.
Harmer, with five sixes, traded maximums with Doug Bracewell off the beleaguered Kent spinners before the New Zealander was stumped to prompt the declaration.