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.
Night-watchman Paul Harris was the only batsman to be dismissed Monday, caught at cover off fast bowler 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 on Friday, with the arrival of leading batsman Mohammad Yousuf and the likely inclusion of fast bowler Shoaib Akhtar.
Scoreboard
PAKISTAN (1st Innings) 313 (Younis Khan 68, Yasir Hameed 65; M. Ntini 5-83).
SOUTH AFRICA (1st Innings) 417 (A.G. Prince 138, H.H. Gibbs 94, H.M. Amla 71; Mohammad Asif 5-89).
PAKISTAN (2nd Innings) 302 (Imran Farhat 68; P.L. Harris 4-46).
SOUTH AFRICA (2nd Innings, overnight 69-2):
G.C. Smith lbw b Hafeez 32
A.B. de Villiers c Younis b Asif 12
H.M. Amla not out 64
P.L. Harris c Faisal b Asif 7
J.H. Kallis not out 60
EXTRAS (B-8, LB-4, NB-12) 24
TOTAL (for three wkts, 60.5 overs) 199
FALL OF WKTS: 1-20, 2-67, 3-80.
BOWLING: Mohammad Asif 14-2-56-2 (9nb); Rana Naved ul-Hasan 7-3-21-0 (3nb); Shahid Nazir 3-1-13-0; Danish Kaneria 24.5-5-61-0; Mohammad Hafeez 12-2-36-1.
RESULT: South Africa won by seven wickets.
UMPIRES: S.A. Bucknor and B.R. Doctrove (both West Indies).
TV UMPIRE: K.H. Hurter (South Africa).
MATCH REFEREE: B.C. Broad (England).
MAN-OF-THE-MATCH: Hashim Amla.
SECOND TEST: Port Elizabeth, Jan 19-23.
THIRD TEST: Cape Town, Jan 26-30.—AFP