Masood's brilliant 151 was his first hundred for four years, while Shafique also returned to form with 102 as the pair put on a solid 253-run stand for the second wicket after Pakistan won the toss and batted.
England, led by Ollie Pope in the absence of the injured Ben Stokes, briefly fought back when they removed both Masood and Shafique in the space of just two runs in the third session.
The visitors took the second new ball at 308-3 and dismissed Babar Azam, trapped leg-before by fast bowler Chris Woakes for 30. Saud Shakeel was unbeaten on 35 at the close of play with nightwatchman Naseem Shah yet to score.
England's attack toiled hard in the Multan heat, with fast bowler Gus Atkinson the most successful with 2-70. Woakes and spinner Jack Leach both took a wicket each.
Masood had been under pressure to make runs, with his last hundred coming against the same opponents at Manchester in 2020 - 14 Tests and 27 innings ago.
He pushed Woakes for a single to complete his fifth Test hundred off just 102 balls with two sixes and 13 fours in a dominant display of batting.
Shafique was equally assured as the pair made England's three-pronged pace attack and two spinners toil on a batting-friendly pitch.
"Thanks to the management that they backed me in my lean phase," he said.
"I am happy that I have contributed today. As a batting unit, we have done well but we still need to carry on tomorrow."
'Pretty happy'
Assistant coach Jeetan Patel was satisfied with the hard work put in by England's bowlers.
"The toil the bowlers put in today was great," said former New Zealand spinner Patel. "They tried different things to take wickets, with different fields."
"We are pretty happy with what we have ended up with. We would have liked them six down or all out but it's a sub-continental pitch."
England took a wicket in the fourth over when Atkinson forced opener Saim Ayub to glove a shorter ball down the leg side to wicketkeeper Jamie Smith with the total on eight.
The visitors thought they had a second when pace bowler Brydon Carse, on debut, trapped Masood in front on 16 and umpire Kumar Dharmasena gave him out.
However, a review showed the ball had pitched outside the leg stump.
Masood went on the attack against Shoaib Bashir, hitting the off-spinner for four boundaries before two more off Atkinson took him to his 11th Test 50.
Shafique survived being run out on 34 when Pope missed the stumps with his diving throw with the batsman well short of his ground. He smashed two fours and a six off Bashir to reach his sixth Test half-century.
Both teams have picked three fast bowlers and two spinners, hoping that the pitch will offer new-ball help to the seamers before taking spin later in the match.
The remaining Tests are in Multan (October 15th-19th) and Rawalpindi (October 24th-28th).
