Zaheer, left out of the Indian team for the first two matches of the seven-match one-day series against Sri Lanka at home, bowled a devastating spell after West took 108-run firstinnings lead.
West, 37 for two in their second innings, now need just 76 runs to register an outright win on the last day tomorrow.
Jacob Martin (16) and first innings centurian Wasim Jaffer (8) were at the crease when the stumps were called for the day.
Earlier, resuming at their overnight first innings total of 314 runs for 8, West Zone were all out for 327 runs and gained the vital first innings lead of 108 runs.
K S Shahbuddin and L Balaji were the main wicket takers for South by taking three scalps each.
In their second innings, opener Robin Uttpappa (52), captain V V S Laxman (69) and Hemang Badami (47 not out) showed some resistence to the otherwise lacklustre batting by the South batsmen.
After losing two wickets at 16 runs, Utthappa and Laxman took the total to 91 before Utthappa was brilliantly caught by keeper Parthiv Patel off Zaheer.
After his departure, Badani joined Laxman and together they played coutiously but the former had to leave the field when he was on 25 and the team score at 158 after he received injuries on his head following a Sairaj Bahutule throw.
Soon after, Laxman was sent back on his individual score of 69 runs as he could not read the delivery of speedster Munaf Patel and was clean bowled.
Then the South Zone wickets fell like a pack of cards.Badani then returned after taking some treatment and tried to take his team to a comfortable score but could not get supportfrom the other end and the entire team was bowled out for 211 runs.
West Zone, needing 113 runs for an outright win, started their second innings on a distrous note losing two wickets when the scoreboard read just 9 runs.
However, later Jaffer and Martin ensured that the team doesn't lose another wicket and took the team's total to 37 runs.