England were 302 for seven at stumps on a rain-marred second day after Bess had made 49 in a match the hosts had to win to end the series all square at 1-1.
That left England 128 runs ahead after they had dismissed Pakistan for a meagre 174 on Friday.
Jos Buttler, dropped on four, was 34 not out and debutant Sam Curran unbeaten on 16.
After rain meant there was no play before lunch on Saturday, England resumed on 106 for two -- a deficit of 68 runs.
England captain Joe Root was 29 not out on his Yorkshire home ground and Bess yet to score, after coming in late Friday following the fall of opener Alastair Cook for a well-made 46.
The overcast conditions -- the floodlights were switched on to guard against bad light -- promised to assist Pakistan's bowlers.
But with England desperate to avoid a third straight Test series loss after reverses in Australia and New Zealand, Bess rose to the challenge again.
The Somerset off-spinner may have still to take his first Test wicket but this innings followed the 20-year-old Bess's commendable 57 on Test debut during Pakistan's dominant nine-wicket victory at Lord's.
Bess cover-drove left-arm quick Mohammad Amir for four, one of several boundaries worthy of a top-order batsman.
But there was fresh frustration for Root, however.
Having often been criticised for failing to convert his Test fifties into hundreds, Root fell for 45 on Saturday when, chasing a scrambled seam delivery from Amir angled across him, he succeeded only in getting a thin edge to wicket-keeper Sarfraz Ahmed, the Pakistan captain.
But when Bess swept leg-spinner Shadab Khan, England had the lead.
England saw their tea score of 199 for three quickly transformed into 212 for five as they lost both Dawid Malan (28) and Bess, who shared a fourth-wicket stand of 62.
Amir struck with his first delivery after tea when a ball of extra bounce took the shoulder of Malan's bat and looped gently to Haris Sohail at first slip.
Bess was on the brink of another Test half-century when, trying to dab a quicker ball from teenager Shadab, he was well caught by Asad Shafiq at slip to end a 95-ball innings that included seven fours.
England should really have been 220 for six when Buttler, who had made just four, stabbed at Shadab only for the ball to burst through Hasan Ali's hands at midwicket.
Not long afterwards, Buttler was hit flush on the helmet by a Hasan bouncer after missing an intended pull shot.
But he hit the next ball for four.
Jonny Bairstow too might have fallen in single figures when he was lbw playing no shot to medium-pacer Faheem Ashraf for eight only to be spared on review by height.
Ashraf did dismiss the Yorkshireman for 21, however, when Bairstow edged to Sarfraz shortly before the new ball became available.
But the last over of the day saw England finish with a flourish as Curran pulled and drove two fours in as many balls off Hasan.
England were in sight of a new record at the close.
No batsman has yet made a fifty this innings.
England's highest Test total without an individual half-century is their 315 against the West Indies at Port-of-Spain in 1986.
First Published: June 3, 2018, 12:37 AM IST