The superior visiting team dismissed Zimbabwe for 163 in 39.5 overs with leggie Amit Mishra producing career-best figures of six for 48. India made short of the modest target, reaching home with 16 overs to spare.
Ajinkya Rahane made 50 in his first match of the series while opener Shikhar Dhawan scored a 38-ball 41. Ravindra Jadeja remained unbeaten on 48 alongside Dinesh Karthik, who was on 10.
India were hardly troubled on the tour but their skipper Virat Kohli thought Zimbabwe gave them a good fight.
"To be honest, the first two games were pretty toughly fought but we stepped up in the next three," said Kohli, who pushed him down the order for his teammates. He did not bat in the last two games.
"It is all about making sure you win the series and then you can experiment. Duncan (Fletcher) told me what to do with batting orders. Most of these guys are going to South Africa (as part of the India A team), and who to give rest was decided by the coach."
"It has been a beautiful thing to be part of this team and now to lead it. This is an eager bunch of 15 who have gone out there and performed. It is a team of very talented players and it has not been that difficult for me as captain," he said of his leadership in the absence of Mahendra Singh Dhoni.
India's start to the chase could have been better. Cheteshwar Pujara failed for the second straight game in a row after Nick Jarvis bowled him in the fourth ball of innings. From there on it was smooth sailing.
All-rounder Pervez Rasool could not get a game in the series, much to the disappointment of the Kashmiris including their chief minister Omar Abduallah.
Earlier, Zimbabwe had little answers to Mishra's turning ball especially the googly. Opener Hamilton Masakadza (32) and Sean Williams (51) were the two who provided some resistance in the middle.
'Look' how the Sheena Bora case has taken a toll on Indrani Mukerjea
Photos: Katrina Kaif, Parineeti Chopra, Shilpa Shetty's movie outing in Juhu
Birthday special: 14 Bollywood actors who made it big on TV
Photos: Vaani Kapoor, Poonam Pandey, Sana Khan at fashion event
Photos: Rishi Kapoor, wife Neetu, daughter Riddhima at book launch