The youngster’s unbeaten 144 from number eight moved the visitors from their overnight 135-4 to the unchartered waters of 448-9.
On a day of firsts, this, astonishingly, was the first time in 25 attempts that the County had reached 400 in an innings and it was the result of a solid effort throughout the order.
Rob Keogh and Adam Rossington made 34 and 27 respectively before James Middlebrook, who finished with 61, joined forces with Duckett in a seventh-wicket partnership of 117.
Duckett exceeded his previous best of 56 and sailed past three figures with his eventual tally of 144 coming from 210 balls.
The declaration came with the lead at 134 and the hosts reduced this by 38, without any damage, in the nine overs they faced before the close.
With their chances of victory extinguished, the hosts will need to bat for the majoroty of the final day to avoid defeat.