Younis was unbeaten on 71 -- also completing 9,000 Test runs -- while Misbah notched an aggressive 87 not out as Pakistan closed the third day on 222-3 on a weary Dubai stadium pitch.
That gives Pakistan an overall lead of 358 with seven wickets intact and makes them favourites for a 1-0 lead in the three-match series on a pitch which will help spinners on the fourth and fifth day.
The first Test ended in a draw in Abu Dhabi.
Younis and Misbah steadied Pakistan from the early loss of three wickets for just 83, adding 139 for an unbroken fourth wicket stand. It was the 14th century plus stand between the two veterans in Tests.
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Younis flicked paceman Stuart Broad to deep fine-leg boundary to reach fifty, hitting seven fours during his 134-ball knock.
When on 47 Younis became the first Pakistan and 14th batsmen overall to complete 9,000 Test runs in his 103rd match.
Misbah smashed two towering sixes off leg-spinner Adil Rashid to complete 50, adding to his brilliant 102 in the first knock. He has so far hit four sixes and eight boundaries off 137 balls.