Sussex were facing a hefty first innings deficit when they slumped to 121 for 7 after lunch on the second day in response to Kent’s 304.
But as the ball got softer so batting became easier and Brown cashed in before he was last out for 90 following a rollicking last-wicket alliance with Jofra Archer.
Archer had taken 7 for 67 on the first day and enhanced his claims as a genuine all-rounder by contributing an entertaining 60 not out to a partnership of 99 which broke Sussex’s tenth wicket record of 77 which had stood since 1905. It helped take Sussex to a total of 291 with Kent reaching 82 for 2 in their second innings, an overall lead of 95.
Brown deserved a century and hadn’t offered a chance until he tried to pull a short-of-a-length ball from Matt Coles which didn’t get up and was lbw after facing 116 balls and hitting 12 fours. Archer played some eye-catching shots off the front foot to lodge his second first-class 50 from 72 balls with ten fours.
Brown also received good support from David Wiese (22), with whom he added 53 for the eighth wicket to take Sussex past the follow-on target before he took the attack back to Kent.
For the first half of an absorbing day Kent’s seamers had held sway. Heavy cloud cover encouraged the ball to swing and it was desperately hard going before lunch for Sussex, who managed only 74 runs in the session and lost four wickets.
Wayne Parnell and Mitch Claydon took two each with Claydon snaring Stiaan van Zyl and Laurie Evans in three deliveries, but skipper Luke Wright showed what was possible in a cameo either side of lunch which brought him seven boundaries in his 29 before he padded up to Coles.
Delray Rawlins, who is making his Championship debut, had belied his lack of experience by batting for more than two hours in the testing conditions before he finally lost patience and chased a wide delivery from Parnell he should have ignored.
Kent seemed to be firmly in control but as their batsmen had discovered on the first day batting got gradually easier and Brown was soon thumping anything remotely short or rocking back to feast on any width in his favourite areas square of the wicket.
Vernon Philander, who was suffering from a groin injury, was absent when Sussex bowled again and Kent openers Daniel Bell-Drummond and Sean Dickson put on 60 before Ajmal Shahzad pinned Bell-Drummond (35) immediately after switching ends and then picked up Joe Denly (3) just before the close.
Sussex coach Mark Davis said: 'Vernon Philander is having a scan on his groin problem in London tomorrow and we should know the extent of the injury then. We'll obviously be guided by South Africa but we'll know more once it's been assessed.
'I thought we fought back well today. At lunch we were five down and definitely behind the eight-ball but Ben Brown played superbly under pressure, as he has done many times for us before. We've made a big thing this season about extending our tail and we know that it's crazy that someone like Jofra Archer is batting at No.11 because he's a special talent and showed that again today to help us drag it back.
'I thought Kent bowled really well but it does get easier once the ball starts to get soft and you can counter-attack like Browny did.'
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