Abhishek, playing in only his second T20 international, lashed 15 boundaries as he scored 100 runs in 47 balls after the World Cup winners won the toss and elected to bat on Sunday, scoring 234-2 in their 20 overs.
Zimbabwe, who pulled off a surprise 13-run win over India in Saturday's opening clash of the five-match series, were bowled out for 134 in 18.4 overs in reply as they never came close to reaching the daunting target.
After completing his half-century in 33 balls, Abhishek took just 13 more deliveries to reach triple figures.
The 23-year-old hit 26 runs off the 11th over, bowled by Dion Myers, and brought up his century with three successive sixes in a display of devastating batting, becoming the first batter to score a century for India in only his second T20 international innings.
"The defeat yesterday wasn't easy for us. I felt today was my day and I made it count," Sharma said.
"As a youngster, you always want to express yourself. I always believe in my ability."
Ruturaj Gaikwad was 77 not out and Rinku Singh scored 48 in other solid contributions for the tourists.
Zimbabwe were never in the chase after losing their first wicket after only three balls while Wessly Madhevere top scored for the hosts with 43.
