Sharma, playing in his second international match, made 100 in an Indian total of 234 for two.
Zimbabwe, who won the first match by 13 runs on Saturday, were bowled out for 134.
The left-handed Sharma, who was out for a duck on debut on Saturday, thrashed eight sixes and seven fours.
"It was a good performance after the defeat yesterday," said Sharma when he was named man of the match.
"Thanks to the coaches and captain to keep confidence."
After opening his score with a six against off-spinner Brian Bennett, who dismissed him on Saturday, Sharma charged to his half-century with a six off medium-pacer Dion Myers.
He then raised his hundred with three successive sixes off left-arm spin bowler Wellington Masakadza before being dismissed next ball, caught at backward point.
Sharma was dropped on the long-off boundary off Luke Jongwe when he had 27.
"After the drop I thought it was my day," he said. "I always believe in my ability. If it's in my arc and even if it's the first ball I will go after it."
Ruturaj Gaikwad (77 not out) and Rinku Singh (48 not out) continued to take the attack to the Zimbabwe bowlers, who conceded 160 runs in the last 10 overs.
India made more runs in their innings than the combined total of both teams in a low-scoring encounter on the same pitch on Saturday when Zimbabwe made 115 for nine and India were bowled out for 102.
Despite an aggressive 26 off nine balls by Bennett, Zimbabwe's hopes were virtually extinguished when they crashed to 46 for four after four overs, with seamers Mukesh Kumar and Avesh Khan taking two wickets each.
India captain Shubman Gill said his young team had responded well to Saturday's defeat.
"Yesterday it was more about not being able to handle the pressure. It is a young side and many of them are new to international cricket. It was good to have pressure in the first game. We knew what to expect in this game."
