Rodrigues and Mandhana, who missed the first two ODIs nursing her injury, gave India a perfect start while chasing a moderate total of 195. During the phenomenal opening partnership - their third century stand so far - the duo registered their respective fifties.
Hayley Matthews got the big breakthrough as Rodrigues was stumped for 69. The southpaw, however, carried on her merry way and became the fastest Indian and third-fastest woman overall to cross the 2000-run mark in ODIs before missing out on her century. Mandhana (74) became Matthews' second victim of the day - caught at extra cover by Afy Fletcher.
Mithali Raj (20) and Punam Raut (24) inched closer to secure the series but with just five runs to victory India lost both the set batters, bringing in Harmanpreet Kaur and Deepti Sharma. Following the hiccup, Deepti hit the winning boundary and took India over the line.
Earlier, a well-compiled 79 by skipper Stafanie Taylor took West Indies to 194 all out after the hosts elected to bat first.
The deciding game of the series saw the return of opener Matthews following the completion of her eight-match suspension. Matthews and Natasha McLean started the innings slowly - the latter struggling with her timing before she fell to Shikha Pandey. Shemaine Campbelle's (7) stay at the crease was also short-lived, as the batter gave a simple catch to Mithali at mid-off off Rajeshwari Gayakwad.
Taylor and Matthews tried to hold together the Caribbean fort, but that ended with an unfortunate decision by the on-field umpire as the latter was adjudged run out. On replay it could be seen that although Matthews (26) was short of her crease, wicket-keeper Taniya Bhatia had knocked over the stumps before she even collected the ball. However, the lack of a third umpire meant the on-field decision had to stand.
Taylor and Stacy-Ann King accelerated in the final 10 overs, combining for a 96 run sixth wicket partnership to take West Indies to a respectable position.
Experienced Poonam Yadav put breaks on West Indies speed as the leg-spinner got the breakthrough, getting rid of Taylor and leaving the hosts at 180 for the loss of six wickets. Soon after, King (38) followed her skipper back to the pavilion as she was cleaned up by veteran Jhulan Goswami. West Indies collapsed towards the end losing four wickets in the last two overs.
Brief scores: West Indies 194/10 in 50 overs (Stafanie Taylor 79, Stacy-Ann King 38; Jhulan Goswami 2-30) lost to India 195/4 in 42.1 overs (Smriti Mandhana 74, Jemimah Rodrigues 69; Hayley Matthews 3-27) by 6 wickets. PoTM: Smriti Mandhana; PoTS: Stafanie Taylor