At lunch, Pakistan were 331 for two in reply to England's first innings 515, a deficit of 184, having saved the follow-on here on Sunday.
Yousuf, whose last two Test hundreds against England had both been double centuries, was 160 not out and Younis 122 not out.
The duo had put on 295 for the third wicket, a record for Pakistan against England.
Neither man gave a chance on Sunday as England's attack looked increasingly listless on a flat, batsman-friendly, pitch.
Instead Andrew Strauss's side, without injured talisman Andrew Flintoff, appeared resigned to their fate and inside an hour paceman Matthew Hoggard, on his home ground, was operating without a slip.
Pakistan, 1-0 down in the four-Test series, resumed on 202 for two with Younis 64 not out and Yousuf 91 not out, after he'd been dropped on five, the duo having come together when their side were struggling at 36 for two.
Yousuf went to his century in style.
He steered Stephen Harmison behind point for four and, three balls later, hooked the fast bowler for six to complete a 145-ball hundred with two sixes and 11 fours in just under three hours.
The six also saw Younis and Yousuf beat Pakistan's previous third-wicket Test record stand against England of 180 shared by Mudassar Nazar and Haroon Rashid at Lahore in 1977/78.
Yousuf's hundred was his 18th in 69 Tests and fifth against England.
Both right-handers were in elegant command as they played the ball late.
Younis pulled medium-pacer Paul Collingwood for four to complete his first Test century against England, and 12th in 46 matches overall, in 171 balls with 15 boundaries.
England appeared to be putting all their faith in the new ball and took it when it became available in the 81st over with Pakistan 303 for two.
But Yousuf responded by twice commandingly driving Harmison, England's quickest bowler, to the extra-cover boundary.
Yousuf then survived an lbw appeal on 146 from Hoggard and next ball cover-drove him to go to 150, with Alastair Cook hurtling over the boundary boards in a vain attempt to stop the ball.
It left England thinking of what might have been if Collingwood had held a low slip catch offered by Yousuf off Harmison with Pakistan 42 for two on Saturday.
England's total was built around a stand of 141 between Kevin Pietersen (135) and Ian Bell (119).
Bell's hundred was his third in as many Tests after his 100 not out at Lord's and 106 not out in England's innings and 120-run second Test victory at Old Trafford.