Amla raised his half century off 95 balls by pulling leftarm paceman Junaid Khan to square leg for four and has spent over 3 hours at the wicket.
Duminy also showed no signs of rustiness as he returned to the test team after more than a year on the sidelines nursing an Achiles tendon injury and was little troubled.
The much trumpeted offspinner Saeed Ajmal has yet to make an impression on the slow wicket of Sheikh Zayed Stadium despite bowling 17 overs for 34 runs.
Irfan had provided Pakistan early breakthroughs after South Africa captain Graeme Smith won the toss and elected to bat first.
Irfan dismissed Alviro Petersen (3) and Smith (15) to have the South Africans reeling at 19-2. Petersen was caught at short leg and Smith returning to international cricket after ankle surgery in May was adjudged caught behind after Pakistan successfully called for a television referral against the South African captain to reverse onfield umpire Rod Tucker's original decision.
Wicketkeeper Akmal grabbed a well-judged catch when Kallis also returning to international cricket since playing in IPL in May got an inside edge off another left-arm fast bowler, Junaid Khan.
Pakistan awarded test caps to Shan Masood on his 24th birthday and to 34-year-old leftarm spinner Zulfiqar Babar, who replaced injured spinner Abdul Rehman.
Pakistan captain Misbah-ul-Haq brought Babar into the attack ahead of Ajmal, but Amla lifted the spinner over the extra cover for a rare boundary in the first session.
South Africa packed its bowling lineup with four seamers led by world No. 1- and 2-ranked test pacemen Dale Steyn and Vernon Philander, Morne Morkel, who is playing in his 50th test, and allrounder Jacques Kallis.
South Africa, which has not lost an away test series since a defeat to Sri Lanka in 2006, thrashed Pakistan 3-0 in a test series at home in February.