At stumps on the second day, Pakistan were 202 for two, still 313 runs behind England's first innings 515 and needing a further 114 to avoid the follow-on.
Younis though was 64 not out and Yousuf, dropped on five, 91 not out after Pakistan had collapsed to 36 for two.
"It has become a very flat pitch," Yousuf said. "Me and Younis will try to play hard cricket. If we bat two sessions tomorrow (Sunday) hopefully we'll save the game."
Earlier England's Ian Bell scored his third hundred in as many Tests, the Warwickshire right-hander making 119 and relegating Kevin Pietersen (135) to an unfamiliar supporting role in an interrupted stand worth 141.
"After the one-day series (against Sri Lanka) I just felt I was getting into a touch of form," Bell explained. "I just tried to work on being positive, believing in my own ability and show the bowler you mean business."
Looking at the match overall, Bell said: "Younis Khan and Mohammad Yousuf have played really well. It seemed the wicket flattened out a little bit.
"On this wicket the harder the ball the more it's going to do. As soon as it loses that hardness it's a pretty excellent wicket to bat on.
"The new ball is going to be crucial when we get to it."
In reply, Pakistan - 1-0 down in the four-match series - lost two wickets for two runs in 10 balls before their experienced third-wicket duo held firm.
Younis and Yousuf added 42 runs in the first six overs after tea.
But Yousuf, who scored a double century in the drawn first Test at Lord's, edged several deliveries through the slips.
And left-arm spinner Monty Panesar, who took five for 72 in England's innings and 120-run second Test victory at Old Trafford, saw Younis - on 36 - survive a huge lbw appeal after he missed his arm-ball.
But a Matthew Hoggard no-ball completed a hundred partnership in 111 balls.
Yousuf then drove Hoggard, on his Yorkshire home ground, for three to go to a 58-ball fifty with six fours before a single off Panesar saw Younis to the landmark in 79 balls with eight fours.
And Yousuf regally drove Harmison's first ball from around the wicket to the extra-cover boundary.
Salman Butt and Taufeeq Umar, playing his first match of the series, had put on 34 - Pakistan's best opening partnership in three Tests.
Hoggard, wicketless at Old Trafford, struck when Umar (seven) was caught behind by wicket-keeper Chris Read, in for the dropped Geraint Jones, who took a good diving catch to his left.
Butt (20) was then run out by Pietersen's direct hit from gully after Younis set-off for a tight single.
And Pakistan were almost 42 for three when Yousuf edged Harmison to third slip Paul Collingwood, who dropped a low chance off the fast bowler.
Bell was the first England batsman since Allan Lamb against the West Indies in 1984 to score hundreds in three consecutive Tests in the same home series.
The 24-year-old made 100 not out at Lord's and 106 not out in Manchester.
He was eventually bowled by Danish Kaneria, trying to steer the leg-spinner, having faced 206 balls with 12 fours in four-and-a-half hours.
England's total was then boosted by a ninth-wicket stand of 56 in just 46 balls between Sajid Mahmood (a Test best 34) and Harmison (36).
Persevering paceman Umar Gul led the attack with five for 123, although Pakistan's leading four bowlers all conceded more than 100 runs each.
Pakistan, as at Lord's and Old Trafford, struggled without injured quicks Shoaib Akhtar, Mohammad Asif and Rana Naved.
After Lord's, Bell expected to be dropped for Andrew Flintoff but the all-rounder's ongoing absence with an ankle injury gave him a reprieve.