The Spitfires' 100 per cent record in the South Group appeared to be in jeopardy after they slumped to 90 for four at Lord's.
But Blake (66 not out) and Kuhn (54) blazed an unbroken partnership of 114 from just eight overs to set up their side's fifth straight victory as Kent posted 204 for four.
That target proved to be beyond the home side, who – despite a fifth-wicket stand of 61 between Eoin Morgan and John Simpson – could only muster 176 for seven in reply.
Mason Crane and Liam Dawson shone with the ball before James Vince finished things off with the bat as dominant Hampshire claimed a seven-wicket win over Essex.
Spin bowlers Crane (three for 24) and Dawson (two for 31) ripped through the Essex batting in the middle overs as the Eagles collapsed to be bowled out for 133 in 16.4 overs.
The hosts, having been 81 for one, lost nine wickets for 52 runs in 47 balls, to fall well below par.
Hampshire then knocked off the 134 required inside 14 overs, with Vince hitting an unbeaten 87 off 54 balls to help his side clinch their first victory at Chelmsford for five years.
At Sophia Gardens, Glamorgan were denied a first win as they conceded 32 runs from the final two overs to share the points with Gloucestershire.
AJ Tye changed the course of the match with 38 from 18 balls, including two from the final delivery to level the scores, after Glamorgan spinner Andrew Salter's four for 12 had seemingly given the hosts a firm grip on the game.
Glamorgan had posted 172 for five on the back of opener Fakhar Zaman's 58 from 43 balls.