Steyn was instrumental in bowling Sri Lanka out for 191 to see South Africa hold a 44-run first-innings lead.
Pakistan need 228 runs and have seven wickets in hand to win the match and avoid a 3-0 whitewash against South Africa.
Steyn was also unlucky not to take a wicket as he saw three catches go down off his bowling.
Dale Steyn and Kagiso Rabada took four wickets apiece as Pakistan folded for 294 in their second innings at Newlands, Cape Town.
South Africa finished day one of the second Test on 123/2, trailing Pakistan (177) by 54 runs at stumps.
Amla's 63 not out guided the Proteas to victory but not without a series of scares.
But it was three rapid strikes by his fellow pace bowler Kagiso Rabada that turned the second day on its head in the final session.
Steyn picked up his 422nd wicket against Pakistan in the Boxing Day Test match in Centurion as he sent back opener Fakhar Zaman in the seventh over.
South Africa pacer Dale Steyn put his money on Australia to win the four-match Test series against India.
Du Plessis says he's happy to take advantage of a depleted Australian lineup with some of their best players on the sidelines.
With the ball going a foot above his head and that too at great speed, the skipper showed amazing reflexes in grabbing the cherry out of thin air.
The celebrations from Steyn weren't extravagant as he knows that the ODI series against the home side will bring him far more prized scalps.
The South Africans lost a wicket on the first ball of the match and were all out for 173 after winning the toss and electing to bat.
Amla is still recovering from a finger injury while Duminy aggravated a right shoulder problem in South Africa's home series against Zimbabwe which will now need surgery.
Steyn made a successful return from injury, coming through two of the three games in the series after having been out of action in ODIs for two years.
Dale Steyn rescued South Africa with his maiden ODI fifty before Tahir bagged six wickets to seal a 120 run-win in a low scoring match.
Captain Faf du Plessis was also named in the squad on Friday but his participation is subject to a fitness test after undergoing shoulder surgery.
In a column that Jimmy wrote for Fox Sports, he gladly states that he was in awe of McGrath's attitude and varied skillset.
Giving out further details of the injury, Cricket South Africa (CSA) said that the bowler has suffered a Grade 1 injury in his right groin.
He, however, asserted that he is still capable of making a useful contribution to the national side.
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