Leg-spinner Shah took 10 for 141, including a second-innings haul of four for 69 on Sunday’s fourth day.
His return, which surpassed Waqar Younis’s previous Test-match best for Pakistan at Lord’s of eight for 154, was central to the tourists going 1-0 up in this four-match series.
Mohammad Amir in his first Test appearance since he was given a five-year ban for his part in the 2010 spot-fixing scandal at Lord’s — Pakistan’s previous Test at ‘the home of cricket’ — ended the match when he bowled No 11 Jake Ball.
Victory prompted the Pakistan team to perform several press-ups in front of the Lord’s Pavilion — a reference to their pre-tour military boot camp.
England, set 283 for victory, were all out for 207.
Delighted Pakistan skipper Misbah-ul-Haq, whose first-innings 114 in his maiden Lord’s Test saw him become Test cricket’s oldest century-maker for 82 years, said: “It is one of the top wins as captain and for Pakistan as a team.
“Everyone bowled well, especially Yasir Shah. We always believe if we cross 300 runs (Pakistan made 339 in their first innings), we are very much in the game.
“We have a top spinner and the bowlers can really put pressure on the opposition.”
Left-arm quick Amir, at the scene of his 2010 spot-fixing crime, ended the match when he bowled last man Jake Ball. Victory saw Pakistan go 1-0 up in the four-match series ahead of the second Test at Old Trafford starting on Friday.
England, chasing 283 runs to win the first game of the four match series, require another 128 runs to win with four wickets in hand. Jonny Bairstow and Chris Woakes are at the crease with 28 and 5 runs to their name.
James Vince was caught by Younis Khan from the bowling of Wahab Riaz after scoring 42 runs from 49 balls after hitting nine boundaries. Gary Ballance was the next English batsman to be dismissed as he was bowled by leg spinner Yasir Shah. He made 43 runs from 66 balls.
The leg spinner got his second wicket as Moeen Ali was bowled while trying to slog the spinner out of the Lord’s ground.
The 42-year-old Misbah added: “It has been a remarkable turnaround after the 2010 incident and the team took responsibility…To win here speaks volumes.”
‘Good kid’ Amir
As for Amir, a teenager in 2010 but now aged 24, Misbah said: “Everybody wants Mohammad Amir to play, especially the crowd.
“He is a good kid now and matured and can prove he is a good bowler.”
England paid dearly for some poor top-order batting in both innings and skipper Alastair Cook said: “There was a bit of naive batting, kind of basic errors.
“It is a tough pill to take, losing at home, but there are three games to go.”
England were holding firm at 195 for six thanks to a determined stand of 56 between Jonny Bairstow (48) and Chris Woakes (23).
But Bairstow’s three-and-a-half hour innings ended when he was bowled trying to whip a Shah leg-break.
That was the cue for a collapse that saw Englans lose their last four wickets for 12 runs in 31 balls.
England’s defeat was tough on Woakes who, in the absence of the injured James Anderson and Ben Stokes, took 11 for 102 in the match.
It was Pakistan’s unheralded left-arm quick Rahat Ali who reduced England to 47 for three on Sunday.
His back-off-a-length ball had Cook (eight) edging through to wicket-keeper Sarfraz Ahmed.
Cook’s opening partner Alex Hales (16) then carelessly chased a wide Rahat ball outside off stump, with Mohammad Hafeez holding a good catch at first slip.
Joe Root struck two superb cover-driven fours off Rahat but the star batsman fell into a hooking trap on nine when he paddled a Rahat short ball to Shah, set back at deep square leg.
James Vince, dropped in the slips, struck nine fours, mainly through the offside, on his way to a Test-best 41 not out at lunch without looking assured.
He had added just one run to his lunch score when, not moving his feet, he edged a booming drive of a Wahab Riaz delivery that moved away to second slip Younis, who this time clung on at the second attempt.
England were making steady progress at 135 for four when leg-spinner Shah, who took six for 72 in the first innings, bowled recalled left-hander Gary Ballance behind his legs for a painstaking 43 with a delivery that spun out of the rough.
Moeen Ali (two) then charged down the pitch in an attempt to drive Shah, only to be clean bowled.
Riaz was unlucky to wicketless during an excellent spell of reverse-swing bowling against Bairstow and Waokes.
Earlier, Pakistan added just one run to their overnight 214 for eight as Stuart Broad cleaned up the tail.
Shah did not add to his 30 but more than made amends with the ball.