Bernard Parker added the second in the second half, for Amakhosi's second win under caretaker coach Ace Khuse.
Chiefs remain sixth on the log, while Ajax remain outside the top eight, as their winless run extends to six League matches.
Chiefs passed the ball around in the opening stages of the match, and on a run down the right, Lehlohonolo Majoro sent in a cross that was cleared by Matthew Booth inside the box. Bernard Parker was picked up the loose ball and passed unselfishly to Letsholonyane, who hit a low shot into the bottom right corner.
The Urban Warriors struggled to get a flow going in the match after that, and Chiefs always seemed in control.
Ajax had just one notable scoring chance in the first half, after a mistake at the back by Josta Dladla, who tried to dribble out of defence and was dispossessed by George Maluleka. The Ajax midfielder's 25-yard shot was saved by Itumeleng Khune.
Just before the half-hour mark, Chiefs had the chance to make it two when Parker again picked up a loose ball, playing it to Siphiwe Tshabalala on the edge of the box.
But Tshabalala's rocket of a shot hit the post, and the match went to half-time 1-0.
Ajax came out the better side, but still squandered possession in the final third. Chiefs looked to hit on the counter, and broke down the right through Jimmy Tau.
Tau played the ball to 'Shabba' in the box, but the Bafana Bafana midfielder's low shot again struck the woodwork.
Six minutes later Chiefs made it two, however, when Tshabalala played a through-ball to Parker, who beat a stranded Sander Westerfeld.
Ajax could not find their feet after the second goal, and the match petered out to a solid win for Chiefs.