Resuming in a strong position at 182-3, the tourists were bundled out for 242 in a dreadful morning session in Dubai.
Joe Root, Ben Stokes and the out-of-form Jos Buttler fell victim to Wahab Riaz's pace, before Yasir Shah's leg-spin bamboozled the lower order.
By the close, Pakistan reached 222-3, a lead of 358 runs, with Misbah ul-Haq 87 not out and Younus Khan 71 not out.
After coming so close to winning the first Test, and contesting the first two days of this match fiercely, this was a hugely disappointing day for the tourists - and one that seriously imperils their chances of getting a result in this series.
Alastair Cook's men will have to hope they can dismiss the hosts quickly on day four, then set about a huge run chase - but their chances of avoiding defeat on a turning fourth-innings track with the wily Yasir in operation appear slim.
England's chances of getting close to, or even overhauling, Pakistan's first-innings total of 378 were always likely to depend on the influential Root - unbeaten on 76 overnight.
But the day got off to the worst possible when the Yorkshire batsman swished at a wide delivery from Wahab and was caught behind for 88.
From then on, England's increasing over-reliance on Root and Cook was horribly exposed as the remaining six wickets tumbled for only 30 runs.
Wahab, bowling with real hostility to exploit England's uncertainty against genuine pace, had Stokes (4) and Buttler (0) caught behind in quick succession in a superb spell of 3-15 in nine overs.
Then it was over to Yasir - bowling in tandem with Wahab for the first 18 overs of the day - who justified his status as the world's top-ranked spin bowler with a display of high-class leg-spin.
Memories of England's awful performances against spin on their last tour of the UAE were revived as Adil Rashid (0), Jonny Bairstow (46) and Mark Wood (1) all perished with poor shots to Yasir.
After conceding a first-innings lead of 136, England desperately needed early wickets, and their seamers got two quick breakthroughs.
James Anderson dismissed Shan Masood (1) for the fourth time in the series before Shoaib Malik (7) was bowled trying to drive Mark Wood.
But England could not capitalise on that good start as their spinners struggled.
Mohammad Hafeez smashed Moeen Ali and Root for sixes before he was caught at slip off Wood for 51.
That brought first-innings centurion Misbah to the crease with Younus - a partnership with a combined age of 78 and one that has thwarted England throughout this series.
Playing cautiously against the seamers and looking to dominate the spinners, the duo - who have now put on a fifty partnership in nine out of the last 10 occasions they have been at the crease together - batted England further and further out of contention.
To win, the tourists will have to surpass the highest-ever fourth-innings chase at Dubai - 137 - and record at least the fifth-highest run-chase this century.
While Stokes is averaging just 24 since the start of the Ashes and Bairstow remains without a Test century, it is the form of Buttler that is the biggest concern in England's malfunctioning middle order.
The wicketkeeper - whose average after his first eight Tests was 52.67 - is averaging just 13.55 in his last seven matches against Australia and Pakistan, with 149 runs in 11 innings.
"Buttler's numbers are not good," said former England captain Michael Vaughan on Test Match Special. "He's got a huge problem: he's not lining up the ball, he's playing it two feet away from his body."
In addition, even his usually reliable keeping faltered as he dropped a simple chance presented by Shan Masood off the bowling of Stuart Broad, and saw another chance fly between him and Joe Root at first slip.
Bairstow is also capable of taking the gloves and James Taylor could replace Buttler in the middle order should England decide to change their side for the third Test in Sharjah.
Ex-England spinner Graeme Swann on BBC Test Match Special: "I think there will be two changes [for the next Test]. The way they're going, they're going to lose unless something ridiculous happens.
"Barring a big score from Buttler or Bell, I think they'll be asked to sit out the last Test. That will allow you to bring in an opening batsman in Alex Hales, and James Taylor at three, with Moeen Ali moving to seven. He's not an opening bat, he showed in Abu Dhabi it's not his natural game."
Michael Vaughan on BBC Test Match Special: "My frustration with England is that they keep having these horrible sessions that lose them the game. Losing seven wickets for 36 runs... it's over. You can say I'm being negative but this game is done."
England require their best-ever fourth-innings run chase to beat Pakistan in the second Test after a dire third day.