Sussex spinner Mark Davis has urged the champions to be patient as they attempt to climb the first division table.
Davis claimed the key wicket of Kent opener and skipper David Fulton at the end of the third day's play to keep Sussex on course for an overdue first home win of the Championship campaign.
The county gave themselves four-and-a-half sessions in which to bowl Kent out after piling up their highest score of the season, featuring centuries from Tony Cottey and Matt Prior plus 88 extras, just 11 short of a world record.
They then removed James Tredwell and the dangerous Ed Smith before celebrating possibly the key wicket.
There were four overs of an intriguing third day left when Davis, whose drop helped Fulton make a century in the first innings, got down sharply to clutch on to a return catch from the same batsman.
Matthew Walker looked like providing the main obstacle as Kent started today still 189 runs adrift with seven wickets left.
Sussex will have plenty of time to finish the job, weather permitting, and Davis said: "The key is to be patient.
"If we can do that and get as many balls in the right areas as possible I'm sure they will be under pressure.
"There's scoreboard pressure and they have only got seven wickets left. We've just got to keep that pressure on them and see what happens."
Robin Martin-Jenkins made the first breakthrough with the ninth ball of his spell straight after tea, Tredwell being judged lbw.
Smith should have followed first ball. This time Martin-Jenkins got the edge but Chris Adams at second slip had two grabs at the chance and wicketkeeper Matt Prior also seemed to lay a finger on the ball before it hit the deck.
Happily for Sussex, Smith never got into his stride and was put out of his misery by a Mushtaq Ahmed leg break before Fulton's rearguard action was ended by Davis.
The catcher said: "It was actually a bit easier than I made it look. He didn't really hit it that hard.
"Hopefully that's a key wicket but there are a few good players still to come so we've still got to work hard."
Prior's cover drive off Ian Butler to bring up his 109-ball century was arguably the pre-lunch highlight as Sussex built on an overnight lead of 66.
The stage had been ideally set for Prior's aggressive strokeplay when he came in at 283-4 on Saturday and he responded with his first Championship century of the summer.
He faced 133 balls and fired 16 fours for his 123 before being picked up by Walker at short fine leg looking to paddle Min Patel away.
Patel also took credit for the two other wickets to fall before lunch, producing an alert return to run out the backing-up Martin-Jenkins, then turning one sharply from leg to off to end Cottey's eight-hour, 362-ball marathon.
Mushtaq hit 22 of a stand of 29 with Davis for the eighth wicket, pulling Patel for six before holing out to long-off from the same bowler as Sussex built a lead of 288.
Their total of 618 was the best ever by either Kent or Sussex in these cross-border tussles. A nice bit of history, but the one which will really count will be if Sussex can complete their first ever home win as county champions.
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