Amir took out all three of India's premier batsmen, bowled a maiden for figures of 6-2-16-3, then watched as his teammates mopped up.
The former captain told Sky Sports 2: "It's a great, great team effort from where we came from because we knew after losing the first game, we were nowhere".
Azhar also continued his fine form in the tournament, reaching his fifty off 61 balls before he was run out following a mix-up with his partner.
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).
Mohammad Amir had Rohit Sharma lbw in the first over and the king of the ODI chase, Virat Kohli came in at 0-1 but instead of steadying the ship he was dropped after just eight balls and instead of taking that reprieve he was out one ball later. In-form Shikhar Dhawan, who was the top scorer in the tournament with 317 runs, also fell to Amir at 21 when he was caught behind in the 9th over.
He hit the Indian bowlers outside the park by smashing six boundaries and an over boundary.
Pakistan have won the Champions Trophy cricket final after beating their arch-rivals India by 180 runs at the Oval ground in Britain's capital, London.
"The extras are something that's never a good feeling to concede so many".
"I mean, 25 extras is a bit too much in a game like that, and that's something that we certainly need to take care of in the future".
"You can always look at things in hindsight, we've always tried to do our best in certain situations, sometimes the opposition does play very well". Ali scored 59 before Mohammed Hafeez provided a late burst with 37-ball 57.
His century set up Pakistan's massive total of 338-4, and they went on to dismiss India for 158.
Praising Pakistan for their brilliant all-round performance in the Champions Trophy final here on Sunday, Indian skipper Virat Kohli said the green brigade can upset any team on their day.
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