The tourists lost stand-in skipper Ollie Pope for a second-ball duck before Zak Crawley and Joe Root steadied the innings with 64 and 32 respectively at stumps.
It was another tough day for bowlers as an unbeaten 104 from Salman and 82 by Saud Shakeel swelled Pakistan's total, which was set up by Shan Masood's 151 and Abdullah Shafique's 102 on Monday.
Pope, standing in for injured skipper Ben Stokes, was smartly caught by a leaping Aamer Jamal who plucked an uppish pull shot off pacer Naseem Shah with one hand at mid-wicket.
He had been drafted in to open the batting after Ben Duckett injured his left thumb taking a catch at the end of the Pakistan innings.
England need another 261 to avoid a follow-on - a task eminently possible on a pitch offering no help to bowlers.
Salman built on the good work of Shakeel and Naseem in the afternoon, reaching his third century with a single off spinner Jack Leach soon after the tea interval.
Salman, who also completed 1,000 Test runs during this knock when he reached 71, added a rapid 85 for the ninth wicket with Shaheen Shah Afridi, who scored 26.
In all, Salman cracked 10 boundaries and three sixes in his 119-ball knock - surviving a catch by Chris Woakes when the third umpire declared the fielder's foot went beyond the rope.
Leach was the most successful bowler with 3-160, while Gus Atkinson finished with 2-99. Woakes, Shoaib Bashir and Root took one wicket apiece.
Salman added an invaluable 57 runs for the seventh wicket with Shakeel, who was caught smartly by Root at slip off Bashir for 82. Shakeel hit eight fours.
Pace bowler Brydon Carse had figures of 2-74 on his debut after trapping Jamal for seven, adding to his first Test wicket of Naseem who was caught at leg slip by Harry Brook before lunch for 33.
Resuming at 328-4, Shakeel and Naseem put on a sedate stand of 64 as England's bowlers kept it tight with just 69 coming in the first session.
The remaining Tests are in Multan (October 15th-19th) and Rawalpindi (October 24th-28th).
