Replying to Pakistan's first-innings 366, England cruised to 211-2 with Duckett and Joe Root looking well set before Sajid (4-86) triggered a spectacular collapse.
England limped to 239-6 at stumps having lost five wickets in the final session including three in eight deliveries.
They are still 127 behind with Jamie Smith (12) and Brydon Carse (two) to the crease.
It was a far cry from their swashbuckling batting earlier in the day when England scored at almost seven-an-over in the first 10.
Duckett (114) led the way, forging 50-plus partnerships with Zak Crawley, Ollie Pope and Joe Root.
The feisty left-hander combined in a breezy 73-run opening stand with Zak Crawley, who led a charmed life before falling for 27.
Crawley survived a run-out after a mix-up with Duckett only because bowler Sajid Khan had broken the stumps before he could collect the ball.
Sajid suffered more disappointment when Crawley was adjudged lbw in his next over but the decision was reversed after replays confirmed the ball would have missed the stumps.
Crawley could not make the most of the reprieves, though, and fell to Noman Ali.
After a caught-behind appeal against Crawley had been turned down, left-arm spinner Noman cajoled his captain Shan Masood to review the decision and replays confirmed an edge.
Ollie Pope (29) made a start too before he was bowled through the gate by Sajid.
With Pakistan unleashing spin from both ends, Duckett found the sweep shot - both traditional and reverse - particularly productive and brought up his hundred with one such shot against Salman Agha.
Root (34), the world's top-ranked Test batsman, added 86 runs with Duckett but fluffed a sweep shot against Sajid and dragged the ball onto his stumps.
Sajid ended Duckett's entertaining knock, which included 16 fours when he had the opener caught in the slips.
Five balls later, the spinner clean-bowled Harry Brook, who smashed a triple hundred in the opening Test.
Noman returned to dismiss England captain Ben Stokes for one to turn the match on its head.
Earlier, Pakistan's lower order chipped in with useful runs after they resumed on 259-5.
Salman Agha (31), Aamer Jamal (37) and Pakistan's number 10 Noman (32) produced defiant cameos to take the hosts past the 350 mark.
Jamal, the lone seamer in the Pakistan attack, suffered a hip injury while batting and has been used sparingly.
England comprehensively won the opening Test, also in Multan, to take a 1-0 lead in the three-match series.
