The visitors closed out the day on 216-6, from being 174-2, and still trail by 162 runs after bowling the home team out for 378 just before lunch.
De Zorzi will resume with Senuran Muthusamy (6 not out) with the Proteas looking to get as close to Pakistan as possible on a pitch that is already turning excessively.
Pakistan started the second day on 313-5 and Mohammad Rizwan and Salman Agha extended their overnight partnership to 163 before Muthusamy made the crucial breakthrough.
The left-arm spinner took three wickets in a one over, including that of Rizwan for 75, and then finished off the innings with figures of 6-117 in 32 overs.
It was Muthusamy's maiden five-wicket haul in his sixth Test appearance while Agha was last man out to Prenelan Subrayen (2-78) for 93, the tourists would have been satisfied with the bowling effort.
Opening pair Aiden Markram (20) and Ryan Rickelton put on 45 before the Proteas captain was caught behind off the bowling of spinner Noman Ali, who then also accounted for Wiaan Wulder (17).
De Zorzi came through a scratchy start, that saw him survive close lbw appeals and edges through slips, to add 94 with Rickelton for the third wicket.
Rickelton looked in sublime touch and made his way to 71 before he was brilliantly caught a slip by Babar Azam off the bowling of spinner Agha.
The wicket sparked a mini-collapse as the Proteas lost four wickets for just 26 runs with Tristan Stubbs, Dewald Brevis and Kyle Verreynne falling cheaply before the close.
The Proteas Women have secured a spot in the ICC Women's World Cup semifinals after the game between New Zealand and Pakistan was abandoned because of rain in Colombo.
Temba Bavuma has been included in the South Africa A side for a first-class fixture next month to prove his fitness ahead of the Proteas' Test series in India.
Pakistan were in with an opportunity for a massive upset against England at the ICC Women's World Cup but the game was eventually abandoned due to persistent rain in Colombo.
The Proteas' 10-match winning streak in Test cricket came to an end after a 93-run defeat against Pakistan in Lahore in the first game of the two-match series.
