David Willey eventually finished Kent off with five for 61, backed up by Jordan Thompson who took three for 24 to give Yorkshire 23 points in Group Three, while Kent took five.
Milnes batted for over four and half hours and faced 210 balls, including an 89-minute partnership with Darren Stevens, who was Kent’s next highest scorer with 47.
Resuming on 33 for two and trailing by 411, the hosts got off to a dismal start when they lost Daniel Bell-Drummond for 24 to the fourth ball of the morning, a spectacular inswinger from Willey that sent his off stump flying.
Joe Denly scored 30 from 33 balls and lingered for the best part of an hour, but he fell to a jaffa from Thompson that was caught behind. Jack Leaning was then out for a duck when he edged his sixth ball, from Thompson, to Tom Kohler-Cadmore at first slip, but Robinson and Milnes survived till lunch, with Kent on 119 for five.
Kent frustrated Yorkshire throughout the afternoon session, with Milnes driving Dom Bess through cover for four to bring up his maiden first class fifty and Ollie Robinson reining in his attacking instincts for a measured 28. Robinson eventually perished when he edged Duanne Olivier to wicketkeeper Jonathan Tatershall, but Stevens joined Milnes to bat through to tea, at which point Kent were 193 for six and harbouring realistic hopes of a draw.
The new ball finally accounted for Milnes, who was lbw to Willey in the 83rd over and he looked a picture of desolation as he trudged off with his head down and his shoulders slumped, not even raising a bat to acknowledge the applause of his team mates on the balcony.
Two overs later Stevens was caught at mid-on by Joe Root off Willey and with Harry Podmore unable to bat, Yorkshire clinched the win with 19.2 overs to spare when the same bowler had Miguel Cummins leg before.
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