Kent assumed complete control on day three of their LV= County Championship Division Two clash with Leicestershire, but may still have to settle for a draw.
After rain ruined the first two days in Tunbridge Wells, Leicestershire began the third day on 74-4 in their first innings and were skittled for 186 before Kent reached 159-1 at the close.
Darren Stevens grabbed a five-wicket haul before Rob Key and Brendan Nash put on an unbroken stand of 144 to take the deficit to just 27 by the end of the day.
The visitors snared Daniel Bell-Drummond (8) lbw through an Ollie Freckingham off-cutter but Josh Cobb's side were otherwise left to rue missing two gilt-edged opportunities.
With Nash on 12, Freckingham rearranged the left-hander's stumps only to hear the umpire's call for a no ball, then Joe Burns spurned a regulation chance at first slip off with Key on 31.
Earlier, Leicestershire were unable to secure a single batting bonus point as they were dismissed for 186 and Stevens returned figures of 5-39 - his first five-wicket haul of the summer.
With the visitors' score on 111 it was Stevens, bowling at the Nevill Ground's Railway End, who started Leicestershire's slide with the scalp of Shiv Thakor (30), caught low down in the gully by Ben Harmison.
Matthew Boyce (17) then shouldered arms to a Calum Haggett off-cutter that pegged back off stump and Cobb (2) departed lbw after an ill-advised flail across the line.
Freckingham (15) sparred at a Charlie Shreck lifter only to spoon a catch to Bell-Drummond low at mid-wicket and Jigar Naik (15) gave Shreck a haul of 3-54 when he feathered one to second slip.
Last man Robbie Williams added 12 to the total before he too edged to second slip to give Stevens the third five-wicket haul of his 207-match first-class career.