India took a 2-1 lead in the five-match series.
Gill hit 66 off 49 balls in an Indian total of 182 for four after he won the toss and decided to bat. Zimbabwe replied with 159 for six.
"It was a crucial win for us," Gill said at the post-match presentation. He added he was delighted with the way India started with both bat and ball.
The win continued an Indian comeback after they lost a low-scoring first match on Saturday. "Everyone is contributing and that is a good sign," said Gill.
India raced to 49 without loss in four overs at the start of a 67-run opening stand between Gill and Yashasvi Jaiswal, then reduced Zimbabwe to 39 for five in the first seven overs of the home team’s innings.
Opening bowlers Khaleel Ahmed and Avesh Khan took three wickets in the power play before off-spinner Washington Sundar claimed two wickets in his first over.
Sundar finished with three for 15 in four overs and was named man of the match.
India were bolstered by the inclusion of their three World Cup squad members, Jaiswal, Sanju Samson and Shivam Dube, who missed the first two matches because of India’s World Cup victory celebrations in Mumbai.
Jaiswal made 36. Samson faced only seven balls towards the end of the innings and made 12 not out. Dube did not bat but conceded 27 runs in two overs of medium-pace bowling.
Abhishek Sharma, who hit a century as an opening batsman in India’s 100-run win in the second match on Sunday, batted at number three and was out for 10.
Zimbabwe captain Sikander Raza bemoaned a poor fielding performance.
"We are proud of our fielding but the wheels came off today. We gave away 20 extra runs," he said.
Dion Myers made a spirited 65 not out off 49 balls as he and Clive Madonde (37) added 77 for the sixth wicket to lift the Zimbabwe innings after their poor start.
