Zaman's figures of 3.3-0-25-0 were ruined only by Hardik Pandya hitting two consecutive sixes.
After losing the toss and being sent in to bat Pakistan started brightly and reached 128 runs before losing their first wicket. Zaman slammed maiden ODI century of his career to lay the foundation for a big total against arch-rivals.
With its win, Pakistan, which came into the tournament ranked No. 8 in the world, has clinched its first Champions Trophy victory.
"It was very disappointing to see that go wrong in the India game".
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.
India, who had demolished Pakistan during the group stage of the tournament, knew they needed an impressive batting display of their own if they were to chase down their target. The other instance came in the 2013 final when India beat England. Previously it was Australia versus India at Wanderers in 2003. He was also removed by Amir. This helped Amir get the outside edge of Kohli - twice.
Amir picked up three wickets for 16 runs from his six overs.
113 sixes were hit in this Champions Trophy, the most in a single edition of the tournament and 10th most overall.
# Yuvraj Singh scored 22 before he was dismissed LBW by Shadab Khan via DRS. In Hasan Ali, the deadliest middle-overs pacer in the world.
After Fakhar caused Azhar to be run out on 59, he took out his frustration on India, notably spinners Ravichandran Ashwin and Jadeja.
# Pakistan's 338/4 is the highest total posted by a team batting first at The Oval.
"We've got two years until 2019 [World Cup] now, we've got the monkey off our back in terms of qualifying, we've got enough points now that we'll not have to go through the qualifying stages, which for us was really important".
Zaman was lucky on Sunday when he got new life after Jasprit Bumrah bowled a no-ball even as the Pakistani opener was caught behind by Dhoni. With the ball we could have had a few more wicket-taking opportunities. Peter Chase's also bowled 11.
For India, Bhuvneshwar Kumar shined with the ball.
Arthur said the focus now shifts to 2019 World Cup.
Pakistan captain Sarfraz Ahmed took the last catch and aeroplaned around the pitch with his arms out before he was swamped by teammates.
So after coming into the tournament as rank underdogs - they entered just edging past West Indies as the lowest seed - Pakistan end up as the victor of the Champions Trophy 2017. Fakhar became the 1st batsman to achieve this feat.
# Fakhar Zaman was dismissed by Hardik Pandya on 114. The collapse continued when left-handed opener Dhawan was caught behind off Amir by Sarfraz.
Pakistan: Sarfraz Ahmed (captain and wicket-keeper), Ahmed Shehzad, Azhar Ali, Babar Azam, Mohammad Hafeez, Shoaib Malik, Hasan Ali, Mohammad Amir, Rumman Raees, Junaid Khan, Imad Wasim, Fahim Ashraf, Shadab Khan, Fakhar Zaman, Haris Sohail.