Pakistan reached tea at 155-1 with Manzoor unbeaten on 72 after he added 135 for the first wicket with debutant Masood who fell after scoring 75.
Azhar Ali was the other not out batsman with seven as Pakistan trail South African first innings total of 249 by 94 runs.
In the morning South Africa were dismissed after adding just four runs to their overnight score of 245-8.
Manzoor and Masood batted with confidence to blunt a four-pronged South African pace attack on a lifeless Sheik Zayed Stadium pitch, reaching 77-0 at lunch.
Masood was the first to reach his maiden half-century, off 102 balls while Manzoor reached his sixth fifty -- third in a row in Tests -- off 96 deliveries.
Masood finally fell, leg-before to part-timer Jean-Paul Duminy after hitting eight boundaries off 140 balls.
This becomes Pakistan's first century stand since Taufiq Umar and Mohammad Hafeez put on 114 against England in Dubai in January last year, ten Tests earlier.
The Masood-Khurram pair is Pakistan's sixth different combination in seven Tests as they struggled to find a solid pair for several years.
Amla, who made 118, edged one sharp Irfan delivery straight into the hands of slip where Younis Khan held a regulation catch. He hit 13 boundaries off 252 balls and held the South African innings on Monday.
With the catch Younis equalled Javed Miandad's all-time Test catches record for Pakistan with 93. Miandad reached the tally in 124 Tests but Younis was quicker in 85 matches.
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