Elton Chigumbura top scored in Zimbabwe's innings with 41 off 65 deliveries.
KL Rahul and Ambati Rayudu revived India's chase after the visitors lost debutant opener Karun Nair for 7.
Chamu Chibhabha made 13 before losing his wicket to Jasprit Bumrah.
Jasprit Bumrah registered his best bowling figures of 4 for 28 to restrict the hosts to 168.
Barinder Sran picked up two wickets for 42 runs in his 10-over quota.
KL Rahul became the first Indian to score a century on ODI debut as his 100 not out helped India beat Zimbabwe by nine wickets to take 1-0 lead in the three-match series.
Ambati Rayudu added unbeaten 62 to the 162-run stand that helped India go 1-0 up with a nine-wicket win.