Fakhar shared an opening stand of 128 with Azhar Ali and, after a mix-up that saw Azhar run out, sprang to life.
Pakistan added 91 runs to their total in the last 10 overs to set India a target that had never been achieved in the final of an ICC tournament.
Hasan Ali matched Amir's three, taking the wickets of MS Dhoni, Ravichandran Ashwin and JJ Bumrah.
Kohli said there was flicker of hope when Hardik Pandya started punishing the Pakistan attack.
Amir was nearly unplayable at times. They conceded 12 wides/no-balls in the first 11 overs (13 wides and three no-balls in total).
He trapped Rohit Sharma lbw for nought with a swinging delivery and removed India talisman Virat Kohli with another fine ball which the captain could only edge to point for five. Kohli was dismissed for 5 runs followed by Shikhar Dhawan for 21.
The collapse continued when left-handed opener Dhawan was caught behind off Amir.
By the time Pandya was run out in the 27th over following a frightful mix-up, the match was as good as done and dusted. As Virat Kohli said in the post-match conference, it was just the probing, aggressive bowling display by Pakistan that did the Indian batting in.
"Obviously your best effort is to try and do it every time, but cricket is not about doing well in every game that you play".
India's lineup remained unchanged for the match, whereas Pakistan replaced Rumman Raees with Muhammad Amir.
India blew the chance to seal a clean sweep as victory would have made Kohli's team world No.1 in one-day and Test cricket.
But this crazy-good Pakistan side had other ideas. First, Pakistan's batsmen batted brilliantly on a good batting wicket and did not let Indian bowlers settle in the middle.
Hardik Pandya smashed 76 off 43 balls, hit half a dozen of sixes to provide some entertainment, before being run-out due to a terrible mix-up with Jadeja.
Incoming batsman Babar Azam kept on supporting the 27-year-old in-form batsman by giving him the strike. Fakhar Zaman scored an entertaining, cavalier hundred before Mohammad Amir starred with the ball as Pakistan drew a line under years of hurt, beating India by an emphatic 180 runs in the final.
In only his fourth one-day global at the age of 27, after his debut just 11 days ago, Fakhar overcame his nervy start to unfurl a series of increasingly assured strokes among his 12 fours and two sixes in a 92-ball century.
A miss-hit, however, sent Zaman back to the pavilion.