Their record-breaking stand of 363 appeared to have left England, 1-0 up in the four-match series, on the backfoot.
But England, who'd made 515 in their first innings, recovered to take three wickets for four runs in 10 balls shortly before tea.
However, a match of fluctuating fortunes saw Pakistan's last wicket pair of Shahid Nazir (13 not out) and No 11 Danish Kaneria (a Test best 29) put on 42 in 66 balls to take their team to 538 and a first innings lead.
Left-arm spinner Monty Panesar led England's attack with three for 127 from 47.4 overs.
England survived the two overs to stumps to be three without loss in their second innings, a deficit of 20 runs, with Marcus Trescothick unbeaten on nought and captain Andrew Strauss three not out.
"I think it's 50-50," said Younis, 28, when asked about the match situation. "If we take some wickets early morning it could be 70-30 in our favour.
"I wanted to lead by example. I'm the vice-captain. I wanted to play my shots and encourage our youngsters," added Younis of his innings.
And he said there was no secret to his huge stand with Yousuf. "The key is that all the time we took quick singles."
England all-rounder Paul Collingwood, who took his first wicket in his 64th over of Test cricket when Faisal Iqbal was lbw for nought, said: "They (Younis and Yousuf) put a great partnership on, it was as simple as that.
"We didn't think the game was running away from us. We just knew we had to keep going and, once we got the breakthrough, put pressure on the new batsman.
"Thankfully, we got that run out and we had a crazy five minutes."
However, the Durham medium-pacer said there was plenty of time for further twists and turns. "There's a long way to go, in two days a lot can happen."
Yousuf fell eight runs short of what would have been his eighth double hundred and Younis was run out for 173.
Younis went when, after Pakistan captain Inzamam-ul-Haq called him for a sharp single, he failed to beat Sajid Mahmood's direct hit from mid-wicket.
He faced 286 balls with 22 fours in nearly seven hours at the crease.
And next ball Faisal Iqbal was lbw for nought to Collingwood.
Then Inzamam (26) exited in bizarre fashion when, trying to sweep Panesar, he over-balanced and fell into his own stumps to be out hit-wicket.
But from 451 for six, the last four wickets added 87.
However, when Panesar, much criticised for his fielding, took a low catch on the fine leg boundary after Umar Gul top-edged a hook off Mahmood, Pakistan were 496 for nine.
Kaneria though struck Panesar for six before he was caught off his fellow spinner by first slip Trescothick.
Younis and Yousuf's stand spanned five-and-three quarter hours, the duo joining forces when Pakistan were in trouble at 36 for two before delighting spectators and statisticians alike with some sumptuous strokeplay.
Theirs was the fifth highest stand in Test history against England, beating Jack Fingleton and Don Bradman's sixth-wicket 346 for Australia at Melbourne in 1936/37.
And this partnership was Pakistan's best for any wicket against England, overtaking the 322 for the fourth-wicket set by Javed Miandad and Salim Malik at Edgbaston in 1992.
Yousuf's last two centuries against England had both been turned into double hundreds - 223 at Lahore in December and 202 in this series's drawn opener at Lord's last month.
But on 192 he gloved fast bowler Stephen Harmison down the legside to wicket-keeper Chris Read.
Yousuf batted for 344 minutes, facing 261 balls with two sixes and 25 fours.
Younis was equally as commanding as his fellow right-hander, the apir elegantly dismantled a listless England attack, missing injured all-rounder Andrew Flintoff, on a flat pitch.
But things might have been different had Collingwood taken a low slip chance Friday off Harmison when Yousuf was on five and Pakistan 42 for two.
Scoreboard at stumps on the third day of the third Test between England and Pakistan at Headingley here Sunday:
England 1st Innings 515 (K Pietersen 135, I Bell 119; Umar Gul 5-123)
Pakistan 1st Innings (overnight: 202-2)
Fall of wickets: 1-34, 2-36, 3-399, 4-447, 5-447, 6-451, 7-481, 8-489, 9-496, 10-538
England 2nd Innings
To bat: A Cook, K Pietersen, P Collingwood, I Bell, C Read, M Hoggard, S Mahmood, S Harmison, M Panesar
Bowling: Mohammad Sami 1-1-0-0; Umar Gul 1-0-3-0;
Umpires: Darrell Hair (AUS), Billy Doctrove (WIS)
TV umpire: Nigel Llong (ENG)
Match referee: Ranjan Madugalle (SRI)