Fakhar capitalised on a lucky escape to strike a superb 114 and lift Pakistan to a commanding total of 338 for four.
Fast bowler Amir ripped out India's top three batsmen before the defending champions subsided to 158 all out.
Pakistan - the lowest-ranked team at the tournament - batted first after India won the toss and left India needing to produce the highest successful run chase in the tournament's history to lift the trophy for the third time, but within three overs their reply was in tatters as Amir produced a devastating spell of bowling.
He trapped Rohit Sharma lbw for nought and removed India talisman Virat Kohli with another fine ball that the captain could only edge to point for five.
Kohli, the world's top-ranked one-day batsman, had been dropped off the previous delivery in the slips and the India fans looked shell-shocked as he trudged off.
Their hopes now rested largely on the shoulders of Shikhar Dhawan, who had been in fine form in the tournament, but he made only 21 before nicking the inspired Amir to wicketkeeper Sarfraz Ahmed.
Spinner Shadab Khan snared Yuvraj Singh lbw for 22 and Dhoni, India's former captain, who has saved the team on many occasions, pulled Hasan Ali to Imad Wasim at deep square leg to depart for four.
Shadab picked up his second wicket when Kedar Jadhav, on nine, gave Sarfraz a simple catch and India appeared to be crumbling meekly at 72 for six.
Pandya, however, briefly raised their spirits with a quickfire 76, reaching his 50 with three successive sixes off Shadab and hitting six maximums in all before he was run out.
Jadeja nicked Junaid Khan to slip for 15, Hasan had Ashwin caught by Sarfraz and Hasan forced Bumrah to lob another catch to the wicketkeeper, who pouched it gleefully to complete Pakistan's first Champions' Trophy win with 19.3 overs to spare.
Just R20 for the first month. Support independent journalism by subscribing to our digital news package. 