Kent will aim to complete their first County Championship win since April on Thursday.
A rain-interrupted day saw the hosts extend their second-innings advantage against Lancashire at Canterbury.
They will resume on the final day with a lead of 215 runs, and effectively four wickets remaining.
Although rain wiped out much of day three, with only 38.3 overs bowled, Jaydn Denly hit 74 as Kent built their lead
Opener Ben Dawkins added just a single to his overnight 35 when he edged Will Williams to Keaton Jennings at slip, but the players went off for rain shortly after.
When play resumed Tom Bailey sent Denly’s off stump flying, but a further downpour resulted in an early lunch, with the score 131-2.
After a delay of more than two hours, play resumed with George Balderson switching to the Pavilion End and having Joey Evison caught behind for 26.
Joe Denly, in as a concussion substitute for Tawanda Muyeye, cracked Mitch Stanley (2-56) for six over mid-wicket to take Kent to 170-3 at tea. But he rarely looked comfortable and was caught behind for 19 after flashing at the same bowler.
Stanley had Harry Finch lbw for four before the rain returned at 5.12pm. With no prospect of a resumption, play was abandoned for the day, with Ekansh Singh unbeaten on a patient 30 and Mo Rizvi yet to score.
Singh said: “I think we’re pretty pleased. Obviously, it’s not been the easiest of wickets to bat on, so we bowled really well, I thought yesterday.
“Our first innings got a decent score and we’re in a pretty good position now to go on tomorrow. Still a lot of hard work to go, but I feel like we’ve put ourselves in a good position to go and win the game.
“I’m seeing it well. It’s always nice. It can come and go at times, but it’s nice to be seeing it well at this time with a couple of games to go at the end of the season.”
Report from ECB Reporters Network supported by Rothesay