"The way Jimmy (Anderson) and Broady (Broad) fired in there puts us in a very strong position."
Pakistan, who lost their 2006 series in England 3-0, saw their three wickets fall for one run in a frenetic seven-ball sequence. Broad had figures of two for 14 and Anderson one for one from four overs.
Pakistan coach Waqar Younis said: "I haven't given up on the Test match but it seems like it is going to be very, very hard from here.
"But this is a four-Test series and we won against Australia (after losing the first Test) and showed we are a very fine side."
It was a see-sawing day in which Pakistan started by saving the follow-on when Umar Gul scored an exhilarating 65 not out from just 46 balls.
They needed eight runs at the start of play. England then slumped to 98 for six but Prior's third test hundred calmed the nerves.
Even though England held a first innings lead of 172, Prior's runs were important and took England to 262 for nine declared, effectively batting Pakistan out of the match.
His 136-ball effort ensured that Pakistan need to surpass the world record successful run chase of 418 that West Indies made in 2003 against Australia.
Pakistan's highest-ever fourth innings score to win is 315, also against Australia, in 1994.
Prior, dropped from England's one-day plans earlier this year, combined in valuable partnerships of 49 with Graeme Swann, 56 with Broad and then 49 with last man Steven Finn. He said he was not affected by pressure before his innings.
"There's always pressure," he said. "International cricket is about pressure, how you respond to it and how you adapt to it.
"I've not played a day for England as batsman-keeper not under pressure. I'm very used to it and actually enjoy it and thrive on it."
Prior was on 63 when Finn came to the crease and as he approached his century he took a single off the first ball of an over seven times but the number 11 batsman survived for his nine not out from 50 deliveries.
Prior said: "I had a huge amount of confidence (in Finn), because we've just played a county game against each other where I had to watch him get a 35-ball nought not out when they were eight down - and that was thoroughly annoying.
"As he walked to the wicket today, I said something along the lines of 'same again please, mate.'"
The floodlights were switched on all day after play began under gloomy skies, but they stayed on long into the evening session despite bright sunshine breaking out.
Gul claimed three wickets in England's second innings after earlier entertaining spectators with his stroke-play. His innings contained eight boundaries and four sixes.