Jeev Milkha Singh (73) was tied 55th, while SSP Chowrasia missed the cut by a shot with rounds of 75 and 71.
Raphael Jacquelin took a one-shot lead into the final round, moving ahead of Anthony Wall in the closing stages of day three at the Donnafugata Golf Resort and Spa.
Kapur had 12 of the 14 fairways and 15 greens in regulation, but needed 31 putts during his 69.
He had birdies on first, fourth and seventh, which made up for the double bogey on the par-three third. On the back nine, he bogeyed the 11th, but eagled the 16th.
Jeev struggled on the opening 10 holes with bogeys on second and eighth and then a double bogey on 10th. Birdies on 12th, 16th and 17th was some consolation but the bogey on 14th meant he was 73 for the day.
Jacquelin and Wall had threatened to turn the event into a two-horse race when they pulled clear of the chasing pack.
However, both dropped shots down the stretch to leave the tournament wide open.
Atwal misses cut
Indian golfer Arjun Atwal missed the cut at the Transition Championships after carding a disastrous eight-over 79 in the second round here, following his 69 in the first round at Innisbrook, Copperhead.
Atwal’s total of 148 was way off the cut, which came at one-under 141. Justin Rosetook a one-shot lead after the third round.