Kane opened the scoring in the third minute, but then clipped the post with a 72nd-minute penalty, won by Vardy, after Hakan Calhanoglu had equalised to score Turkey's first goal against England in the teams' 11th meeting.
Leicester's Vardy given one-game ban
Vardy rode to the rescue in the 83rd minute, as the Leicester City hitman slamming home his third England goal in three games to end Turkey's unbeaten run in 13 matches and enhance his claim to a spot in manager Roy Hodgson's starting XI in France.
"Wins are always pleasing and there were some positive aspects," said Hodgson, whose side face Russia, Slovakia and neighbours Wales in the group phase at the Euro.
"Some large swathes of the game we played reasonably well, but there was also a positive because we're not the finished article and there's still work to be done.
Leicester's Vardy given one-game ban
"It showed the next three weeks will be vital for us."
In a patchy England display, Hodgson saw Jack Wilshere play for 66 minutes in his first international game since last June after missing almost the entire season with a fractured shin, while Jordan Henderson continued his recovery from a knee problem as the Arsenal man's replacement.
Hodgson, who was missing his Manchester United contingent and all of Liverpool's players bar Henderson due to club commitments, confirmed that Vardy will miss Friday's game against Australia in Sunderland as he is getting married on Wednesday.
Hodgson names his final 23-man squad for the Euro after the game.
Playing in Euro 2016 would be ‘pinnacle’ of my season, says Vardy
Sunday's match had been billed as an audition for the strike partnership of Kane and Vardy, the Premier League's top two English scorers, but the Leicester star started on the left in a narrow 4-3-3, with Raheem Sterling on the opposite flank.
A sparse crowd at the home of Manchester City saw England take an early lead.
Sterling found Dele Alli and he smuggled a pass between Mehmet Topal's legs to Tottenham Hotspur colleague Kane, whose assured finish into the bottom-right corner was allowed to stand despite an apparent offside.
Television pictures appeared to show Turkey coach Fatih Terim using his mobile phone to show fourth official Daniel Siebert the evidence, but to no avail.
It was a goal that highlighted England's speed of thought and foot in attack, but Turkey's equaliser 10 minutes later exposed Hodgson's problems in defence.
Oguzhan Ozyakup's pass down the inside-right channel set Volkan Sen scampering in behind left-back Danny Rose.
The Fenerbahce midfielder beat the sliding Joe Hart to the ball and crossed for Bayer Leverkusen's Calhanoglu to sweep home from close range.
After Cenk Tosun had given England a couple of scares, the hosts switched to a diamond midfield on the hour, with Vardy joining Kane up front and Sterling taking up the number 10 role.
Vardy showed what he could do in a central position by surging clear and inviting a challenge from Topal that encouraged referee Deniz Aytekin to point to the spot.
Kane's spot-kick grazed the left-hand post and went wide, but Vardy netted the winner from close range after goalkeeper Volkan Babacan collided with Ismail Koybasi as he attempted to field Gary Cahill's back-post header.
Turkey substitute Olcay Sahan almost equalised at the death, but his volley drew a superb one-handed save from Hart.
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