Mishra has bamboozled the Zimbabwe batsmen throughout the series and recorded figures of six for 48 as the home side collapsed to 163 all out.
India chased down the modest total with ease, with Ravindra Jadeja hitting a massive six to complete the game with seven wickets still intact and 96 balls left in the innings.
"The first two games were very well fought out by Zimbabwe, but the guys stepped it up in the next three and we are pretty happy with the performance," India captain Virat Kohli said.
"Belief is key. All these 11 guys who played on the field believe that they can win games all by themselves and that is a big thing in international cricket. It has been a beautiful thing to be part of."
India won the toss and elected to field first in overcast conditions that suited the bowlers. Only Sean Williams (51) put up any sort of fight for the Zimbabweans, with Hamilton Masakadza (32) the only other player to get out of the teens.
Mishra's six wickets took his tally for the series to 18 at an average of just 11, more than double the next highest Indian wicket-taker, Jaydev Unadkat, who managed eight. India lost Cheteshwar Pujara (0) in the first over of their reply, bowled by Kyle Jarvis who took two for 18 in eight overs, but never looked troubled in their chase.
Shikhar Dhawan (41), Ajinkya Rahane (50) and Jadeja (48 not out) provided a solid base for the thumping win.
"We have been outplayed by a very good team and there haven't been too many positives," Zimbabwe captain Brendan Taylor said.
"We have been way below our best as a team and individuals. It's tough to swallow,"
"Our mental approach is our biggest issue. Maybe our mindset is not all there when we are trying to build a partnership as batters. That is an area we can work with.
"The batters have not come to the party, but our bowlers can hold their heads up high."
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