The hosts were 2-225 at the close of play, still trailing the tourists by 133 runs after an absorbing day of at Old Trafford.
A gutsy half century from the injured Rishabh Pant helped India post 358 in their first innings at Old Trafford, with England captain Ben Stokes' first five-wicket Test haul in eight years helping see off the tourists' tail.
Crawley and Duckett moved at a rapid rate before tea to eat into India's total as England's reply got under way, but neither could convert their impressive starts into centuries, the pair falling for 84 and 94 respectively in the evening session.
Joe Root and Ollie Pope survived several close calls to see England through to the close, putting the hosts in with a chance of sealing victory in the five-match series with one Test to spare.
Resuming the day on 4-264, Pant appeared in the India dressing room in his whites after retiring hurt on Wednesday trying an audacious reverse scoop shot when on 37, before heading to hospital for scans.
After England fast bowler Archer removed Ravindra Jadeja for 20 early under grey Manchester skies, and Shardul Thakur (41) followed him back to the pavilion, Pant received a standing ovation as he surprisingly limped down the steps and onto the field.
Running between the wickets was difficult, but Pant, effectively on one leg, steered the tourists through to lunch on 6-321.
As play restarted, the battling Pant pulled out the big shots. He slogged Archer for six before moving past fifty, his 18th in Test cricket, with another boundary.
After Stokes had removed Washington Sundar and debutant Anshul Kamboj, Archer ended Pant's resistance by sending the injured wicket-keeper's off stump flying for 54. Pant has now amassed the most runs by a wicketkeeper in a series on English soi
Duckett continued where Pant left off when England came to the crease in reply, scoring at over a run a ball as he reached his 15th Test fifty in the evening sunshine.
Crawley quickly followed, his 23rd score of fifty or more helping England's opening pair pass their century partnership for the fifth time as a duo.
The partnership was ended at 166 as Crawley was caught in the slips by KL Rahul having achieved his highest ever test score against India.
Duckett did not last much longer, Kamboj snaring his maiden Test wicket, to leave the batsman six short of a ton.
Pope offered up several catchable chances, with Root surviving two loud lbw appeals.
However, both added more runs into the final over, setting things up nicely for more thrills and spills on Friday.
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