After electing to field, India dismissed the home side for 114 before chasing down their target with 27 overs remaining in a comfortable win to take advantage in the three-match series.
Five Indian bowlers took wickets, but it was Yadav who stood out as he dismissed West Indies' top scorer Shai Hope (43) and tore through the tail in a devastating spell, finishing with figures of 4-6.
He was aided by Jadeja, who took the wickets of Shimron Hetmyer, Rovman Powell and Romario Shepherd.
India lost opener Shubman Gill (7) early in their reply, but Kishan (52) combined with Suryakumar Yadav, Hardik Pandya and Jadeja to see India to within sight of their target before Jadeja and captain Rohit Sharma took them over the finish line.
"Never thought we'd lose five wickets but it was a good chance to give a chance to a lot of the guys who have just come in," said Rohit, who came in at number seven.
"I thought restricting them to 115 got us in a commanding position that we needed so we thought we could give those guys a chance who haven't played a lot in the last few weeks."
The second ODI will be played at the same venue on Saturday.
