Glamorgan started the day 30 behind but Ingram and Kellaway batted sensibly for the morning session to take their stand to 172, by far the best first-innings effort on either side on a slow wicket.
They were happy to accumulate singles and put the odd bad ball away, with little sign of a wicket apart from a run-out chance to dismiss Ingram.
The South African, who will be taking a coaching role in the One Day Cup, looked set for a third successive hundred but fell on the stroke of lunch, as he edged the left-arm spin of Jaydn Denly to slip after hitting nine fours and a six.
Kellaway drove Parkinson to cover just after the interval, having taken his season’s Championship tally to 749 in another mature knock from the 21 year old.
That encouraged Daniel Bell-Drummond to delay taking the new ball and Parkinson repaid his faith as the old Kookaburra grew ever more difficult to get away, with Timm van der Gugten clubbing him to mid-wicket and James Harris lobbing a return catch.
But Ned Leonard hoisted Parkinson for a couple of straight sixes either side of the second batting point, secured in the company of a cautious Chris Cooke.
Remarkably Kent bowled an extra 17 overs before eventually taking the new ball at 316-8, and Agar bowled Leonard for 25 with the fifth ball of his spell.
Cooke was last out for 36, skying Parkinson to mid-off after trying to farm the strike, leaving time for Kent to cut the deficit by 14 runs before tea.
Jaydn Denly led a mostly untroubled reply from Kent, helped by seeing key seamer Timm van der Gugten withdraw for most of the third session.
But Denly, whose uncle Joe is likely to bat low down if needed with a calf injury, lost patience and hoicked Kellaway high to mid-wicket for 38.
Compton reached a placid 38 not out off 109 balls and Benjamin was unbeaten on 22 overnight after play ended on time for once, with Kent needing to bat through day three at least and hope the pitch wears in the final innings.
BBC News
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