Dhawan struck 116 as India recovered from early jolts to post a competitive 294 for eight and then restricted the hosts to 236 for nine to take a 2-0 series lead in the five-match series.
Put into bat, India were in a spot of bother at 65 for four at one stage before Dhawan and Dinesh Karthik (69) put on 167 runs for the fifth wicket to not only restore the innings but take them to a commanding total at the Harare Sports Club.
The Indians could have won the match by a much bigger margin but a defiant late-order resistance by Elton Chigumbara (46) and Prosper Utseya (52 not out) delayed the inevitable with the duo adding 88 runs for the seventh wicket to frustrate the tourists.
Opener Visu Sibanda (55) also provided a rollicking start to the Zimbabwean innings which somehow lost the momentum after his departure with five wickets falling within a span of 24 runs.
For India, Jaydev Unadkat was the pick of the bowlers with four for 41 while leg-spinner Amit Mishra accounted for two wickets.
The two teams will play the third match of the series at the same venue here on Sunday.
Zimbabwe lost opener Sikandar Raza (20) early into their run-chase as the Pakistan-born batsman, who had top-scored with 82 in the first one-dayer, went for an expensive pull-shot against Unadkat and was holed out in the deep.
Next man-in, Hamilton Masakadza and Sibanda chose to play a more patient game and rotated the strike cleverly before opening up against Vinay Kumar's medium-pace and Mishra's googlies.
Both hit Mishra early on in his spell for a six each while Kumar was pulled for two boundaries in the opening over and was taken for 16 runs in his return over in the second spell as the second-wicket partnership looked threatening on an eased out pitch.