It meant they only managed a single batting point, having begun the game at Beckenham 24 behind leaders Essex.
Opener Sean Dickson made 63 as they reached 146-7 before Will Gidman (51) and Matt Coles (52) led a recovery.
South African paceman Rory Kleinveldt took 3-70 for the visitors, who had made 31-0 in reply by the close.
Kent need to win and hope that leaders Essex slip up against Glamorgan next week before the two meet in the final round of matches.
But their first-innings total means they can take no more than 20 points from the game, so Essex will only need 21 from their two remaining fixtures to clinch the Division Two title.
The day's statistical high point came when Gidman was caught by Kleinveldt off spinner Graeme White, his first dismissal for Kent after three unbeaten half centuries, giving him an average of 283.
Northants were left to face 11 overs in the final session and Ben Duckett (19 not out) and Rob Newton came through them unscathed.
Kent suffered a blow to their promotion hopes as they were bowled out for 230 on the opening day of their penultimate Championship game against Northants.