Pakistan were 160 for four at lunch on Sunday, an overall lead of 56. Inzamam was unbeaten on 22.
Opening batsman Imran Farhat rode his luck to make 68, defying the South African bowlers until shortly before lunch when he was caught at silly mid-off by AB de Villiers off left-arm spinner Paul Harris for a painstaking 68.
The other wicket fell to Shaun Pollock, who trapped Younis Khan leg before wicket for 38. Pakistan's runs came slowly, with only 57 scored in 26 overs before lunch.
The left-handed Farhat, who survived a difficult chance to gully when he had seven Saturday, took most of the morning to advance from his overnight 41 but he was lucky to survive.
Without adding to his score, he edged Makhaya Ntini to Jacques Kallis second slip, with the ball reaching the fielder on the half-volley.
On 47 Farhat was dropped by wicketkeeper Mark Boucher off Ntini when Boucher dived in front of first slip Graeme Smith.
Farhat was almost strokeless against the fast bowlers but was more adventurous against the spin of Harris. But it was Harris who claimed his wicket when he stretched forward and the ball went straight from his bat to De Villiers, standing close to the bat.
Farhat batted for 261 minutes, faced 167 balls and hit 10 fours.
Inzamam looked solid as he saw Pakistan through to lunch with Faisal Iqbal, the side's last specialist batsman.