Niall O'Brien, Ramnaresh Sarwan and Matthew Boyce all struck half-centuries as Leicestershire reached 250-5 in reply to Kent's first-innings total of 406 on day two of their County Championship Division Two match at Grace Road.
Michael Thornely and O'Brien shared a 53-run opening stand before Kent seamer Callum Haggett claimed the first of his three wickets when Thornely chipped a catch to cover for 22.
O'Brien, who was dropped on 22 by Rob Key at slip off Haggett, and Ned Eckersley put on 80 in 16.2 overs for the second wicket.
Eckersley - who was left on 99 not out when rain washed out the final day of last week's draw against Hampshire - hit 10 fours in his 56-ball 46.
Haggett (3-57), the ex-Somerset all-rounder making his County Championship debut for Kent, removed Eckersley and O'Brien (63) in successive overs to reduce Leicestershire to 138-3.
That became 155-4 when Mark Davies (1-34) bowled Josh Cobb for eight but Sarwan and Boyce forged a 95-run stand for the fifth wicket to revive the home side.
Sarwan edged behind off Darren Stevens (1-18) for 54 to bring the day to a close, with Boyce unbeaten on 53.