Overnight leader Canizares (73) found water twice on the last three holes to end on eight under as Kaymer's level-par 71 proved enough to take the lead.
England's Steve Webster was tied for second with Canizares after a 70.
Another Englishman, Luke Donald, carded a 67 to join a group of six players in fourth, another shot off the pace.
Northern Irishman Rory McIlroy (69) was a further two shots back, joined by a quartet of Englishmen - Richard Bland (67), Danny Willett (69), Graeme Storm (71) and Kenneth Ferrie, whose round-of-the day 65 featured an impressive eight birdies.
After bogeying his first hole, Kaymer could hardly have imagined he would top the leaderboard by the end of the rain-delayed day's play.
But the German now believes he can repeat last year's summer double when he won the French and Scottish Opens back-to-back.
"Next week is one of my favourite courses, so why not?" speculated Kaymer, who also bogeyed the fifth hole but made up shots at the second and ninth.
"This is one of the biggest tournaments we have on the European Tour. To win it once is big, but to win it twice would be awesome."
Canizares and Webster, who was left to rue a double bogey on the par-three second, are both chasing a spot at the Open, which begins on 15 July.
One place in the St Andrews field will be awarded to the leading non-exempt player, providing he finishes in the top five.
For Canizares, the son of former Ryder Cup player Jose Maria, it would be a first major - after 10 failed attempts to qualify for the Open and US Open.
And his nervous finish at Le Golf National in Paris on Saturday does not bode well for Sunday's crucial final 18.
Leading by three strokes at the time, the 27-year-old pushed his tee shot into the lake at the short 16th to eventually double bogey.
And then his one-shot lead disappeared when he failed to make the carry on the 470-yard 18th as he dropped another two strokes.
Donald, who sank six birdies on Saturday, has finished second, first and third in his last three starts on the European Tour.
However, he aims to stick to his plan of playing predominantly in the US.
"I do enjoy coming over, but it would be a pretty big upheaval to play more in Europe," said the 32-year-old.
"We have a baby, our home is in America and to spend more time here would be tough. I want to play against the best and most of the time the PGA Tour has stronger fields."
McIlroy, meanwhile, was not ruling out a similar final-round flurry to the 62 that won him his maiden PGA Tour title at Quail Hollow in May.
"I feel like I have a low one in my, but I'm struggling on the greens this week," said the 21-year-old.
Welshman Rhys Davies was a stroke behind McIlroy after managing an eagle on the par-five third on his way to a 67.
Lee Westwood's mediocre week continued as he went round in 71 to lie three under.
Ian Poulter could not build on his second-round 67, also firing a 71 for the same total as Westwood.