The prolific Babar has now reached a half-century in five successive Test innings, with his previous five matches yielding four hundreds.
England coach Chris Silverwood, speaking to reporters after stumps said: "We know we're up against a very good batsman."
He struck express paceman Archer down the ground before driving Bess for another boundary to bring up Pakistan's hundred.
There was still time, however for Buttler to miss stumping Masood after the batsman charged down the pitch.
But Azhar's decision to bat first was understandable given Pakistan are playing two leg-spinners in Yasir Shah and Shadab Khan, who they expected to be more effective on a wearing pitch.
As was the case during the West Indies series, the three-match campaign is taking place behind closed doors on health grounds, with Pakistan denied the vibrant and vocal support they usually enjoy in England.