The Portugal Under-21 international pounced on Marnick Vermijl's cross in stoppage time and showed great composure to take a touch before ramming the ball into the net.
Although Bebe had stressed he was set to go out on loan against next season, the boss hinted he could be retained in Manchester.
"He had his loan at Besiktas and then picked up a bad injury which kept him out for most of the season," said Sir Alex. "That is probably his first game for about eight months, so he will be pleased to be back playing and pleased scored a goal. "We’ll see how the season progresses for him, but it gives me a headache in terms of number of strikers we have there, but that’s not a bad thing."