The sixth century in a Trophy final ended in the 34th over with Pakistan at 200-2.
The now fit-again Amir removes all of India's top three as the champions slump to 33 for three in nine overs before being dismissed for just 158. Rumman Raees, who filled in for Amir in the England game, will sit out.
Kohli also praised young all-rounder Hardik Pandya, who was the highest scorer among the Indians with 76 runs off 43 balls.
Leg spinner Shadab Khan trapped Yuvraj Singh right in front but the umpire denied Pakistan's appeal.
The left-arm pacer extracted movement both in the air and off the pitch and quite a few of his deliveries were nearly unplayable.
After winning the toss, Indian skipper Virat Kohli said that they are not taking Pakistan for granted and are looking forward to putting their best foot forward.
By the time Pandya was run out in the 27th over following a disgusting mix-up, the match was as good as done and dusted.
The Pakistani bowlers, who have done very well since after the early India match, came in with all guns blazing.More news: Boeing closing in on US$5bil orders from Asian airlines
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CONDITIONS: Another batting paradise is expected and will help the batsmen play their shots on the up.
For a team that can t play global cricket at home due to security issues, the victory has far-reaching implications. Two of those have been in this tournament, one by England a year ago and the other was by India in 2007.
But it was wins all the way from then on, culminating in Sunday's stunning success at The Oval - the scene of Pakistan's first Test match victory in England in 1954.
He celebrated with an extravagant twirl of his bat and kissed the turf as the Pakistan supporters sensed an unlikely win.
But this crazy-good Pakistan side had other ideas.
The duo forged 128-run partnership in 23 overs before a running mix-up cost Pakistan a wicket. We wanted to be a lot more consistent.
Fakhar Zaman reached to his magnificent hundred in thirty first over as he became the only Pakistani batsman in Champions Trophy 2017 to score a hundred. Ravindra Jadeja (8-0-67-0) and Kedar Jadhav (3-0-27-1) leaked 164 runs in 21 overs and scalped just a wicket.
Pandya in an effort to build the innings after the huge collapse turned on his aggressive mode as he thumped Shadab for three sixes and a four in the twenty third over. "We have to identify the players we want to take forward", he added.
At that point it really was embarrassing for Pakistan and seemed to give them little to no chance of qualifying for the semi-finals with India and South Africa expected to dominate the group.