Rahul was one of three ODI debutants selected for the clash in Harare, with Karun Nair and Yuzvendra Chahal also making their bows in the format.
Chahal (1-27) was among the wickets as Jasprit Bumrah (4-28) starred with the ball to help dismiss Zimbabwe for 168 after the hosts had been put into bat.
But it was Rahul who stole the show with an excellent innings, which he capped off with a six to bring up his ton and seal a dominant victory as he finished unbeaten on 100.
Six of Zimbabwe's batsmen reached double figures, but none scored at anywhere close to the necessary pace in a laborious innings.
Elton Chigumbura top scored with 41 off 65 balls, however, Zimbabwe largely had no answer for Bumrah, who was ably supported by Dhawal Kulkarni and Barinder Sran (both 2-42) in throttling the home side's batting line-up.
Nair (7) went cheaply in an early blow to India's chase of their meagre target, but that was the only blot on a wonderful innings with the bat for the tourists, Rahul and Ambati Rayudu (62 not out) powering them home with 45 balls remaining.
Rayudu's measured half-century was his sixth in ODI cricket but the day belonged to Rahul, who sailed a six over long on to bring up his 100 and get India over the line.
He becomes the 12th man and the first Indian to reach three-figures on his ODI debut, joining a list that includes Ricky Ponting and Martin Guptill, and will aim to guide the visitors to a series win in Monday's second meeting.