Kapur was four shots behind the leaders, Francesco Laporta, Thomas Linard and Jason Scrivener, all of whom shot 68 each.
Laporta and Linard posted the only two eagles of the day at the Robert Trent Jones-designed Royal Golf Dar Es Salam, where scoring was tough with only 32 players breaking par in testing conditions.
Kapur, coming off a tied 5th finish at the Panasonic Open in Japan, did extremely well to recover from a start that saw him go three-over after three holes with a bogey on first and a double on third.
"I am happy with the way I fought back after the start, when I went three over within three holes," said Kapur.
"The conditions were tough but a great challenge but I feel I am playing well as my last two finishes have been in Top-10 at Hero Indian Open and Panasonic, so I hope I can improve on that this week."