Playing his first ODI tournament, the 27-year-old left- hander got a "life" when he was batting on four as Jasprit Bumrah overstepped despite MS Dhoni taking a simple catch behind the stumps.
Zaman made full use of the opportunity to punish the Indian attack on a day when it mattered most.
His 114 off 106 balls had 12 fours and three big sixes with the maiden ton coming off only 92 balls.
By the time Ravindra Jadeja took a well-judged catch off Hardik Pandya to remove Zaman, the team's total had reached 200.
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The final flourish was provided by veteran Mohammed Hafeez (57 off 37) with help of four boundaries and three sixes. He added 71 for in 7.3 overs with Imad Wasim (25 no off 21).
To add insult to injury, India bowled 13 wides and three no-balls in what was a woeful day for all, save Bhuvneshwar Kumar (1/44 in 10 overs).
He got a few streaky boundaries upfront but then settled in to give each Indian bowler, a mighty thwack.
There was no looking back after that and was liberal help from all the Indian bowlers, who erred in length, gave away needless extras to release the pressure completely.
In humid conditions and on flattest of decks, Kohli decided to field first but his bowlers did not do justice to the faith he had shown in them.
The second Powerplay (Overs 11-40) were fully utilised by Pakistan, who scored 191 runs and bulk of those came off the spinners.
Jadeja was guilty of not varying his pace. He bowled too quick and too flat which made strokeplay easier.
Zaman's batting didn't have the grace that one normally associates with left-handers but on a true pitch where hitting through the line was easy, it suited his style.