Portuguese striker scored in stoppage time to save Sir Alex Ferguson's team from defeat - with the hosts dominating proceedings in the second half and grabbing a deserved lead
The striker pounced on a loose ball in the South African side’s area to fire into an empty net after keeper Sander Westerveld and his defenders were beaten by Marnick Vermijl’s accurate cross.
Ajax thought they had won the game in the 87th minute when Alcardo van Graan looped Khama Billiat’s cross over Ben Amos and into the net after beating his marker inside the six-yard box, but the 22-year-old’s strike saved Sir Alex Ferguson’s side from defeat.
Sir Alex made several changes from the United team that beat AmaZulu 1-0 in their opening pre-season fixture, with starts handed to Shinji Kagawa, for his full debut, Anderson and Antonio Valencia.
Paul Scholes, Michael Carrick, Rio Ferdinand and Javier Hernandez also retained their places from the opening game.
The Red Devils struggled for rhythm in the early stages of the match, often giving the ball away cheaply in the final third of the pitch, with Anderson being particularly wasteful when in an advanced position.
Ajax Cape Town should have taken the lead when Billiat was played behind the United defence and put one-on-one with Ben Amos, but he could not find the target when unleashing a left-footed effort.
The home side were looking dangerous and Sir Alex’s men were grateful to Tyler Blackett for making a great block to deny Thembinkosi Fanteni’s goal-bound effort after the striker had found space inside the area.
United finally carved out an opening in the 34th minute when Wootton raided down the right and hit a sublime cross towards the penalty spot to find Hernandez who, in turn, headed the ball towards goal but Westerveld made an excellent save in tipping the effort round the post.
Carrick and Scholes were struggling to take control of the midfield with many misplaced passes often putting the visitors on the back foot, with Paul Rusike taking full advantage when intercepting and starting a counterattack which led to the midfielder hitting the bar from the edge of the area.
United came out in the second half with more impetus and Kagawa, who was anonymous for most of the opening period, came to life and found Hernandez with a lovely through-ball but the Mexican slipped at the crucial moment spurning the opportunity.
Valencia was finding space on the right with ease and he used this freedom, along with his pace, to float a cross towards an unmarked Hernandez, only to see the ball evade the striker by inches.
The Red Devils were really starting to hit their stride and should have taken the lead through Kagawa – only for the Japan international to inexplicably miss the target with a header from five yards out.
Despite United’s dominance in the second half, Ajax still looked dangerous on the break and Fanteni almost broke the deadlock after being put behind the opposition defence, but Amos was equal to his shot and made a good save to turn the ball past the post.
And the hosts finally made their pressure count by taking the lead with just three minutes left to play when Van Graan met Billiat’s corner and managed to loop the ball over Amos into the net, much to the delight of the home crowd and his team-mates.
However this joy was short-lived as Bebe latched on Vermijl’s cross to fire a right-footed volley into the net from six-yards to save the Red Devils' blushes.