Having set the hosts a 283 victory target after their second innings was ended on 215 in the morning, Pakistan's bowlers, led by leg spinner Yasir Shah, provided a masterclass to bowl England out for 207.
Mohammad Amir, back from a five-year ban for spot-fixing, sealed victory when he clean bowled Jake Ball.
England had never chased down such a total at Lord's and while Jonny Bairstow was at the crease they appeared to still have a chance but he was undone by Yasir when he was two short of his half century.
The end was nigh after that as the final three wickets went down for 11 runs.
Pakistan's players celebrated victory by doing press-ups in front of their jubilant supporters.
"It is one of the top wins as captain and for Pakistan as a team," captain Misbah-ul-Haq said. "I am very proud of the team and the way they came out and showed really good skills.
"Today, mentally everybody was strong, and were patient. Everyone bowled well, especially Yasir Shah."
England began the chase confidently with Alastair Cook striking a boundary off his first ball, but the skipper was dispatched after he stabbed at Rahat Ali's delivery and was caught by Sarfraz Ahmed.
