Shan Masood (125) was the only Pakistani batsman to fall on Tuesday, having added a remarkable 242 runs with Younus to turn the match on its head after Sri Lanka had seized control.
Shot out for 215 in the first innings and reeling at 13-2 in the second, Pakistan's stunning victory also saw them jump three places up to third in the test rankings.
"This series means a lot to me. It was a dream, after losing two-three series here," Misbah said at the presentation ceremony.
"The way they (Younus and Masood) played, they almost took the game away from Sri Lanka. And once you have this sort of partnership at the top, it was an easy job for us," he added.
Pakistan began the final day needing 147 for a memorable win and off-spinner Tharindu Kaushal drew Masood out of his crease with flight and turn to have him stumped.
The opener had earlier survived a strong caught-behind appeal when he was on 120 with bowler Angelo Mathews and wicketkeeper Dinesh Chandimal convinced he had edged it.
Umpire Ian Gould, however, deemed otherwise and Sri Lanka moved on having exhausted both of their review opportunities.
Younus continued to play with his characteristic fluency and was unbeaten after registering his 11th 150-plus score in test cricket, the most by any batsman from his country.
The 37-year-old batted for more than seven hours in a man-of-the-match display, also becoming the first batsman to score five fourth innings centuries in test cricket.
"It was not easy," Younus said. "But I have my own expectations from myself, to do well when the team is under pressure. I take the onus on myself to take my team to victory."
Mathews, who struck a defiant century in Sri Lanka's second innings, did not hide his disappointment.
"I thought at 376, we were sitting pretty but that was not the case. We'll take definitely a lot of time to digest this defeat," the all-rounder said.
Pakistani leg-spinner Yasir Shah, who claimed 24 wickets in three matches, won the man-of-the-series award.
(Reporting by Amlan Chakraborty in New Delhi; Editing by Sudipto Ganguly/John O'Brien)
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