New Urban Warriors signing Ndiviwe Mdabuka scored the game's decisive goal early in the second half as Pirates wasted several chances to put the game to bed.
The Buccaneers enjoyed the majority of possession and chances in a first half limited on goalmouth action but not lacking in spirit.
Ajax had a half-chance early on that went over the bar from range when debutant Mdabuka could not capitalise from the edge of the area following a mistake in defence by Tshepo Gumede.
Sifiso Myeni had the first glimpse of goal for Pirates in the 16th minute. Myeni received Luvuyo Memela’s pass in the box, beat one defender and then pulled the trigger but Anssi Jaakkola produced a good save.
Jaakkola had to be alert again just after the half-hour mark to prevent a one-on-one with Thabo Rakhale, who was bearing down on goal after being played clean through.
On 36 minutes Patrick Phungwayo intercepted a stray pass and played Majoro in towards the byline. The striker executed a perfect backheel into the left-back’s path as he rushed into the area but it was on his unfavoured right foot, his touch took it towards a defender, and the chance was lost.
Then four minutes before half-time Majoro had a sight of goal after being played through by the skilful Memela. From the right channel Majoro cut inside the last defender onto his left foot but then fired over the bar.
Early in the second half came the sucker-punch for Pirates as Mdubuka gave Ajax the lead against the run of play. A looping defensive clearance was instincively kept alive by Riyaad Norodien, who played it towards the edge of the area where Mbabuka was lurking, and the former Vasco da Gama man produced a solid albeit slightly deflected finish past a helpless Brighton Mhlongo.
Menzi Masuku was brought on for Pirates to add something extra going forward and he had the best chance to pull Bucs level when in the 80th minute, backtracking at the far post five yards out, he failed to convert a Ntsikelelo Nyauza cross from the right.
Masuku had another half-chance that was blocked by a defender as Pirates chased the gamem while the Sea Robbers had a penalty appeal waved away when Majoro was adjudged to have gone down too easily in the box.
Majoro, who was substituted for 26-year-old Africa Sport Youth Academy graduate Siphamandla Dlamini in the 68th minute, was guilty of wasting the best chances to score on the night. He twice failed to punish Rivaldo Coetzee, first after the defender's poor back-header gifted him a one-on-one which he missed, and then when he dispossessed the centre-back on the edge of the box but then tried two dummies instead of shooting.
Substitute Mpho Makola, who also had a half-chance when he played a one-two with Masuku before being smothered in the box by Jaakkola, had another penalty appeal denied in the 94th minute after the Ajax keeper saved at his feet. Jaakkola got the ball, but it could have gone either way.
Lehlogonolo Masalesa, who was on the reserves bench, was shown a straight red card for something he said to fourth official Daniel Bennett during stoppage time.
