Sent in to bat, India made a cautious start before Jadhav blazed an unbeaten 105 from 87 balls to propel the tourists to 276 for five in their 50 overs.
The home side lost wickets at regular intervals and were bowled out for 193 in the 43rd over.
India looked in trouble when they slumped to 82 for four but Jadhav, batting at number six, at first steadied the innings and then increased the scoring rate with some superb shots.
His highest score in three previous ODI matches was 20, but he found his rhythm in Harare, smashing 12 fours and a six while the other batsmen on both sides found boundaries hard to come by.
Jadhav added 144 for the fifth wicket with debutant Manish Pandey, who was last man out for 71 from 86 balls.
Zimbabwe battled from the start of their reply with only opener Chamu Chibhabha offering any sort of resistance as he reached a second half-century in two matches with 82 from 109 balls.
Stuart Binny, who has had a fine series with bat and ball, was the pick of the Indian bowlers and recorded figures of three for 55 from his 10 overs.
Harbhajan Singh, returning to ODI cricket in this series for the first time in four years, bowled tidily again for two for 35 from his 10.
The teams will begin a two-match Twenty20 series on Friday at the same venue.