Yousuf was last man out for a sparkling 83, made off 90 balls, in an otherwise dismal batting performance on Friday.
Makhaya Ntini and Jacques Kallis took four wickets each as Pakistan collapsed after being sent in to bat.
Yousuf and Mohammad Sami shared the only worthwhile partnership of the innings, putting on 60 for the seventh wicket off only 58 balls, of which Sami made four.
With the teams locked at 1-1, South African captain Graeme Smith gambled successfully that his fast bowlers would be able to make early inroads on a pitch which he believed had some moisture. Eight of the batsmen dismissed fell to catches behind the wicket or in the slips.
Pakistan made a bright start when nine runs were scored off Dale Steyn's first over, including two fours by Mohammad Hafeez, but the rest of the morning was an uphill struggle for the batsmen.
Hafeez was caught by AB de Villiers at third slip for 10 when he got a thick edge to a lifting delivery from Ntini, who struck again when he had Yasir Hameed caught by Kallis at second slip for seven.
Kallis replaced Steyn and took a wicket in his second over when left-handed opener Imran Farhat (20) was squared up and edged a catch to Smith at first slip.
Younis Khan, one of the heroes of Pakistan's five-wicket win in the second Test in Port Elizabeth, fell for eight when he chased a wide ball from Kallis and De Villiers leapt high to take a spectacular catch at second slip.
Captain Inzamam-ul-Haq was caught behind off Andrew Hall soon after lunch and was quickly followed by Kamran Akmal, caught at third slip off Dale Steyn.
Yousuf went on the attack and dominated his stand with Sami, playing some flamboyant strokes. He was able to steal the strike with audacious running which twice in successive overs led to four overthrows being scored as South African fielders took hasty throws at the stumps.
When Sami was caught behind off a top-edged hook against Kallis the tail crumbled quickly, with the last four wickets falling for seven runs in 19 balls.
Yousuf was last man out when an attempted lofted drive off Ntini spiraled to deep mid-off where Ashwell Prince took the catch.
Ntini took four for 44 and Kallis four for 42 as Pakistan were bowled out in just over three-and-a-half hours, with an early tea being taken.
Smith's decision to send Pakistan in was bold on a pitch which seemed likely to give help to the spinners later in the match, particularly at the southern Wynberg end, which was virtually bare. The Kelvin end had a fair covering of grass.
South Africa made three changes, with Boeta Dippenaar coming in as an opening batsman and De Villiers moving down the order to take the place of the suspended Herschelle Gibbs at number six.
All-rounder Shaun Pollock was rested, with Hall taking his place, while Steyn was picked ahead of Andre Nel in a switch of fast bowlers.
Pakistan made one change, with Shahid Nazir replacing injured fast bowler Shoaib Akhtar.
Pakistan Ist innings 157 all out (Mohammad Yousuf 83, Imran Farhat 20; Ntini 4 for 44, Kallis 4 for 42) Vs South Africa