Root, unbeaten on 76, built the innings after England lost the key wicket of skipper Alastair Cook as they fought hard against a pace-cum-spin Pakistan attack on a Dubai stadium pitch.
With Root was Jonny Bairstow on 27 as England were 196 behind Pakistan's first innings total of 378 with seven wickets intact.
The first Test in the three-match series ended in a draw in Abu Dhabi last week.
They built on the early loss of Moeen Ali (one) and Ian Bell (four) and challenged Pakistan's superior bowling attack.
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Cook reached his 45th half-century with a flicked boundary off paceman Imran Khan before he was caught off a leg-side push off the bowling of Shah.
Cook hit 10 well-timed fours during his 117-ball stay.
Root was more aggressive, taking a single off Shah to complete 15th fifty to continue his excellent form in 2015 in which he had already passed the 1,000-run mark before this series.
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Pakistan seamers Wahab Riaz and Imran Khan had given their team an early breakthroughs in the post-lunch session.
Ali was smartly snapped up at short-leg off Riaz while Bell edged one from Khan before Cook and Root led the fightback.