Shah (3-63) and Babar (2-38) took advantage of a wearing Dubai stadium pitch and had England on 187-6 after they resumed on 130-3.
At the break Ben Stokes was on nine and Adil Rashid on eight. England need a near-impossible 304 more runs for victory, or must bat out the last two sessions for a draw.
Pakistan had set England a daunting 491-run target and look favourite to take a 1-0 lead in the three-match series after the first Test ended in a draw.
Root completed 3,000 Test runs when he reached 61 with a single off Riaz towards square-leg. He completed the milestone in his 34th Test and became the 41st English batsmen to score 3,000 or more runs in Test cricket.
But Babar did not take long to dismiss Root with a sharp turner which took the edge of his bat towards the slips, where Younis Khan took a low catch.
Root hit six boundaries off 171 balls.
Jos Buttler survived for 26 deliveries before Shah had him caught by Younis in the slips for seven.
The third and final Test starts in Sharjah on November 1.
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