Paul, who had picked six for 46 in the first innings, was the wrecker in chief once again claiming six for 56 to bowl out the Zimbabweans for 221 in their second innings.
The Indians, who had taken a 213-run first innings lead, knocked off the 12 runs required in 2.3 overs for their second win of the tour.
Earlier, an unbeaten 101 by captain Sairaj Bahutule had enabled the Indians to declare their first innings at 413 for nine, in reply to the hosts score of 200, on the third days play at the Harare Country Club ground.
For Zimbabwe, E Chigumbara top scored with 69 while Alistair Maregwede made 68 as they added 115 runs for the fifth wicket and lead Zimbabwe 'A's recovery from 29 for four in the second innings.
Meanwhile, the senior selection committee has named Andhra all-rounder Venugopal Rao and wicketkeeper-batsman Naman Vinay Kumar Ojha of Madhya Pradesh as replacements for India 'A' cricketers Rohan Gavaskar and Dinesh Karthik who have been picked for the senior team.
The two replacements will join the India 'A' team, that will play a triangular One-day series in Kenya from August 11 to 21 and last two four-day matches against hosts Kenya from August 26 to September 4.
The 'A' teams of India and Pakistan and the Kenyan national team are in the fray in the tri-series.