Opting to bowl in chilly conditions, the Indians had the home team on the mat from the very first over. Sean Williams (51) was the only Zimbabwean batsman to put up a semblance of fight before the home team's innings folded in 39.5 overs.
In reply, India were 43/1 in six overs which were bowled before the innings break. Ajinkya Rahane (7) and Shikhar Dhawan (34) were at the crease for the visitors.
Mishra was the top wicket-taker for the visiting side with six for 48 in 8.5 overs.
Mishra also achieved a record in the process. With 18 wickets in the series, he equalled Javagal Srinath's record for most wickets in a bilateral series.
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Srinath took 18 in seven games in New Zealand in 2002-03, while Mishra has taken 18 in five games here.
The collapse started pretty early for Zimbabwe with opener Vusi Sibanda (5) getting caught behind the stumps by Dinesh Karthik off Jaydev Unadkat in the fourth over.
Next man in skipper, Brendan Taylor, departed without troubling the scorer but consumed 11 balls in the process. He was caught by Suresh Raina at second slip while trying to have a go at Mohit Sharma.