Amla (64 not out) and Kallis (60 not out) put on an unbeaten 119 for the fourth wicket as South Africa made light of what coach Mickey Arthur had expected to be a difficult task on a wearing pitch.
Leg-spinner Danish Kaneria, who had been expected to be Pakistan's dangerman, gained some sharp turn at times but was unable to take a wicket in 24.5 overs which cost him 61 runs.
Amla was beaten twice in the first over of the day by Kaneria but played the spin bowler with increasing confidence as he built his innings.
Nightwatchman Paul Harris was the only batsman to be dismissed Monday, caught at cover off Mohammad Asif for seven.
Play started 45 minutes late because of a wet outfield caused by overnight rain.
South Africa, who resumed at 69 for two, lost Harris in the sixth over of the day when he drove Asif uppishly and Faisal Iqbal held an easy catch.
Kallis, South Africa's most experienced batsman, started cautiously before batting with confidence and taking over as the senior partner, while man-of-the-match Amla played a sound supporting role in making his second half-century of the match.
The pair added 119 off 227 balls and were seldom trouble, especially in scoring the 77 runs they still needed after lunch.
South Africa set up the win when they took a 104-run first innings lead despite batting second, with a century by Ashwell Prince and half-centuries by Amla and Herschelle Gibbs making the bulk of the runs.
Pakistan are likely to be strengthened for the second Test, which starts in Port Elizabeth Friday, with the arrival of leading batsman Mohammad Yousuf and the likely inclusion of fast bowler Shoaib Akhtar.
Pakistan 313 and 302 lost to South Africa 417 and 199 for 3 (Hashim Amla 64 n o, Kallis 60 n o, Graeme Smith 32; Mohd Asif 2 for 56, Hafeez 1 for 36) by 7 wickets