Just three runs had been added to Worcestershire’s overnight total when Nick Potts wrapped up proceedings by catching Gibbon’s edge, with the visitors set 333 to win.
Allison put the hosts into an early stronghold with a double wicket maiden, kissing the edge of Harry Came’s bat and handing a straightforward catch to Rehaan Edavalath at second slip, before striking two balls later when he pinned Matthew Montgomery in front for nought.
Allison heaped on the misery for Derbyshire by claiming his third and fourth wickets of the morning in quick succession, removing Wayne Madsen and Yousaf Bin Naeem to reduce the visitors to 32-4.
The wickets continued to tumble when Martin Andersson saw his 21-ball stay at the crease was ended by Gibbon, before headline act Allison sealed a second five-wicket haul of the match and a third of the season when he celebrated the wicket of Brooke Guest.
Reece and Basra provided some resistance before the interval, holding firm in a 36-run stand that saw the away side limp through to lunch at 75-6.
Reece took a lead role in the afternoon session as he made his way to a gritty 49 from 67 balls but was undone one run short of a deserved half-century when he chopped on to the impressive Allison after mistiming a drive.
Basra saw his off-stump sent cartwheeling after Gibbon nipped one back from over the wicket to end his riposte of 40, and the seamer put the Pears on the verge when he had Shoaib Bashir caught at slip with the very next ball.
The final act of the summer saw Gibbon wrap up victory when he removed Potts for 29, as the visitors were bowled out for 157.
Report supplied by ECB Reporters’ Network supported by Rothesay.