Lancashire's young batsmen staged a spirited fightback on the third day of the Vitality County Championship match at Emirates Old Trafford, but Kent needs just 93 runs from nine wickets to win on the final morning.
Keaton Jennings' side were bowled out for 332 in their second innings, leaving the visitors all out for 164 to win their first game of the season.
Faced with a difficult chase, Ben Compton and Daniel Bell-Drummond made light of the loss of Zak Crawley for one to steer their side to 71 for one at the close. There is little chance of Lancashire winning a match for the first time since 1888, when they beat Oxford University at Old Trafford.
The morning session began badly for Lancashire when Tom Bruce was bowled for 12 when he played down the wrong line to Wes Agar. George Balderson and George Bell then put on a 75-run partnership for the sixth wicket, which only ended when Balderson, who had made a composed 48, attempted to cut a ball from Jack Leaning and was caught by Bell-Drummond at gully.
Balderson and Bell's stand, however, had ensured that Lancashire avoided an innings defeat. Bell and Matty Hurst continued their calm accumulation after lunch.
Bell reached his second fifty of the season on 114, pulling a long hop off Joe Denly to the mid-wicket boundary, only to fall for 65 to Harry Finch, who couldn't avoid a good delivery off Agar to the right of the keeper. But the pair's seventh-wicket stand of 78 had extended their side's lead to 106 and Hurst and Tom Hartley continued the good work, the former reaching his 134-ball fifty with just one four.
Hurst and Hartley put on their side's third 50-plus partnership of the day shortly after tea, but any hopes of Lancashire chasing down a 200-plus target were quickly extinguished when they lost their last three wickets for the same number of runs in 15 balls.
The patient Hurst was caught at slip by Bell-Drummond off Parkinson for 58, Tom Bailey was leg before to Agar for a single and then Hartley was bowled around the legs by Parkinson for 35 to leave the Kent leg-spinner with figures of 3 for 70 on his return to Old Trafford. Agar took 3 for 65 and returned with figures of 7 for 100.
Kent's chase of their modest target began badly when Crawley was leg before to Balderson's seventh ball of the innings. But Compton and Bell-Drummond survived a series of confident appeals, many of them from Nathan Lyon, who bowled superbly and was unlucky not to have at least one success.
And the turn taken by Hartley and Lyon in the evening session suggested that Kent's chase might not be entirely straightforward on the final morning.