Both teams were under pressure after losing their opening matches and a second defeat would almost certainly mean they could not reach the semi-finals.
South Africa captain AB de Villers won the toss and Amla had scored only seven when he slashed a short delivery from Mohammad Irfan to backward point.
Umar Amin, who had replaced Asad Shafiq in the Pakistan team, got the fingertips of his left hand to the ball but could not hold on to the chance.
Amla and Colin Ingram took the total to 53 in the 15th over when the latter was dismissed lbw by off-spinner Mohammad Hafeez for 20 trying to sweep.
Faf du Plessis was caught for 28 off Irfan and Amla fell at the start of the second powerplay when a reverse sweep off spinner Saeed Ajmal lobbed to Hafeez at short third man. His innings had lasted 97 balls and included nine boundaries.
The pressure on South Africa increased when Pakistan captain Misbah-ul-Haq effected consecutive runouts.
Misbah first raced to the bowler's end to whip the bails off when De Villiers slipped while trying to make his ground after he had been sent back by JP Duminy.
He then threw down the stumps at the bowler's end from short mid-wicket when it was Duminy's turn to slip after he was sent back.
The 39-year-old Pakistani was in the action again when he dived to his left in the covers to catch David Miller and there were two further runouts as the South Africans tried to accelerate.