The Proteas took an unassailable 2-0 lead into this contest after a 211-run win in Johannesburg was followed by a four-wicket triumph at Cape Town.
After winning the toss, South Africa's Graeme Smith elected to bat as he began his bid to become the first ever captain to mastermind 50 Test wins.
Smith's first-innings contribution was disappointing, however, the opener amassing just five runs before he was caught at second slip by Younis Khan off fast-bowling debutant Ehsan Adil. The skipper's departure reduced the Proteas to 38 for two after Alviro Petersen (10) had earlier been trapped lbw by Rahat Ali.
Amla and Faf du Plessis set about steadying the hosts with an unbeaten 66-run partnership before the interval, with Amla doing the lion's share of the damage as he hit nine fours on his way to his 27th Test fifty in 78 deliveries.
Du Plessis was equally impressive as he lashed six boundaries in a 42-ball 29.
Both sides made a number of changes to their line-up for the final Test.
South Africa all-rounder Jacques Kallis failed to feature after picking up a calf injury in nets, with fast bowler Kyle Abbott coming in for his debut. Kallis' withdrawal followed that of Morne Morkel, who missed out with a hamstring strain and was replaced by fast bowler Rory Kleinveldt.
Pakistan were forced into a late change when Umar Gul went down with an illness, leaving the star seamer on the sidelines with the dropped Tanvir Ahmed. The duo's absence paved the way for Adil and Ali to start and both responded with wickets.
Pakistan also dropped opener Nasir Jamshed in favour of Imran Farhat.