After resuming on 157-3, Kent superior comfortably sufficient to 171 earlier than Hannon-Dalby hit them with a burst of three wickets for six runs in 14 balls.
Jack Leaning and the half-fit Muyeye had been trapped leg earlier than wicket by inswingers earlier than Charlie Stobo edged his first ball to Rob Yates at second slip.
Ed Barnard then trapped Stewart lbw and adopted up with the wicket of Matt Parkinson, who edged to wicketkeeper Michael Burgess.
Alfie Ogborne edged Michael Rae to slide earlier than Joey Evison, working out of companions, lifted Barnard for six to achieve a 93-ball half-century.
Evison batted impressively in each innings however, in one other try and clear the ropes, he picked out Bears skipper Alex Davies at long-on off Michael Sales space to be final out for 65.