Kent spinner Adam Riley returned career-best figures but his team still had the worst of the second day at the Ageas Bowl where Hampshire finished on top.
Riley, 21, finished with 7-150 having only previously taken 28 first-class wickets, but Hampshire still managed to amass a first-innings total of 455.
In reply, Kent reached 149 for four from 44 overs by the close of the second day, still 306 behind and 157 from the follow-on.
The sunshine and the perfect batting conditions provided the platform for Neil McKenzie and Sean Ervine to extend Hampshire's overnight total of 265 for four from 96 overs.
South African McKenzie raced to the 49th first-class century of a distinguished career and the fifth-wicket pair combined for 189 before they were parted.
McKenzie's 146 was his second-highest score for Hampshire but was ended when Riley found an edge for wicketkeeper Geraint Jones to snare.
The former Test opener faced 214 balls, hitting 21 fours, and it looked as if the patient Ervine would join him in scoring a century until Hampshire lost two wickets in four balls at 403.
Adam Wheater was leg-before sweeping Riley when on 21 and, in the next over, Ervine chased a wide delivery from Darren Stevens and Jones again took the catch.
Ervine hit 10 fours in a 226-ball innings of 86 that was notable for its uncharacteristically subdued creation.
Riley bowled David Balcombe five runs later but Kent were made to wait for the end of their misery as Danny Briggs made a run-a-ball 25 and last man David Griffiths struck Riley for two sixes before being bowled to complete the off-spinner's haul in the same over, the 146th.
With Stevens taking 2-72, the only other wicket-taker was medium-pacer Calum Haggett, who dismissed Briggs.
When Kent responded, openers Sam Northeast and Rob Key made batting look just as easy as Hampshire had done in an opening partnership of 106 in 29 untroubled overs.
But Northeast fell leg-before to Ervine after hitting 10 boundaries in a fluent 59 and was followed back to the pavilion by Key in the next over.
The former England batsman had scored 47 when he edged Griffiths into the slips, where Ervine took the opportunity to reduce Kent to 110 for two.
Griffiths broke through again with the score on 139 when he bowled Daniel Bell-Drummond and Riley's memorable day was ruined when, as nightwatchman, he was caught at short-leg by James Vince off Briggs.
Brendan Nash reached the close unbeaten on 27 alongside Ben Harmison as Kent avoided any further damage.