Nottinghamshire 185 (Moores 49*, Abbas 6-49) and 146 for 6 (Duckett 51, Abbott 4-30) lead Hampshire 231 (Middleton 59, Paterson 3-39) by 100 runs
Opening batter Duckett grabbed a quick-fire 51 which brought a whiff of the panache he showed during his hectic winter with England to the LV= Insurance County Championship.
But Hampshire, who had quickly seen their first-innings of 40 wiped out, reaffirmed their position on the front foot through Abbott's four for 30 - which included three wickets in eight balls.
Newly promoted Notts ended the day on 146 for six - with a lead of 100 on a pitch that isn't getting harder to bat on.
Duckett embraced Brendon McCullum and Ben Stokes' entertaining style to average 56, with a century and four fifties during Test tours to Pakistan and New Zealand - with further successes in the limited-overs formats.
In all likelihood, he will open for England in the one-off Test against Ireland in June and then in the Ashes. But he still needed to start the season strongly.
The closest he had come to "Bazball" then was a dance and swing, but second time around he looked to punish the bad balls with an air of confidence.
He and Haseeb Hameed had scrubbed off Hampshire's 40-run first innings lead within 10 overs using timely aggression. Any width was carved to the offside boundaries with little care for the 13 wickets that had previously been snared behind the wicket.
Hameed guided Barker to first slip, before Duckett reach his half-century in 54 balls. And then Abbott pounced.
Fast bowler Abbott regularly has spells where he becomes unplayable with his bustling nip in both directions. Duckett, Joe Clarke and Lyndon James felt the full force of once such burst just after tea.
The former South African international trapped Duckett lbw before finding Clarke and James' outside edges in a formidable double-wicket maiden - the damage was three wickets in eight balls and Notts sliding from 86 for one to 86 for four.
Ben Slater started watchfully for his 43 before swinging more and more frequently to eventually hole out to deep cover.
Steven Mullaney batted out 63 balls for his 12 before Abbott returned to have him lbw and swing the momentum towards the hosts.
Earlier, Hampshire had gained a first-innings lead but had lost their last seven wickets for 111 runs to suggest they had missed an opportunity to steam ahead - although high-quality bowling rather than poor batting was largely to blame.
Ben Brown and Ian Holland slowly rebuilt with a 47-run stand but both fell to Fletcher - who claimed three for 44.
Olly Stone returned after lunch with verve to pick up Keith Barker and Kyle Abbott to end his first innings as a Notts bowler with three for 82, while South African added James Fuller to claim three for 39.