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Iyer, who missed the limited overs home series against New Zealand, has not yet fully recovered from his back injury.
Rajat Patidar, who plays for Madhya Pradesh in the domestic circuit and Royal Challengers Bangalore in the Indian Premier League, has been named as his replacement.
Ravichandran Ashwin also made gains in the latest rankings./
Riding on the 159-run fifth wicket stand between Pant and Iyer, India, who were left tottering at 94 for 4, will fancy their chances for a fourth-day finish.
The elegant Shubman Gill, who has impressed in limited opportunities in ODIs, is likely to open with Dhawan.
The opener remains unbeaten on 209 as West extended the lead to 319 at stumps on day three.
Kerala pacer Basil Thampi bagged two wickets for the South Zone while Het Patel remains unbeaten on 96.
Among bowlers, Ravi Bishnoi galloped 50 places to take 44th position, and Kuldeep Yadav leapt 58 places to 87th. However, Bhuvneshwar Kumar dropped a spot to 9th.
India defeated West Indies by 88 runs in the fifth T20I having already sealed the series.
Iyer, who was preferred over the in-form Deepak Hooda, Sanju Samson and Ishan Kishan, fell for a four-ball duck in the opening T20I..