Returning to county cricket after Bangladesh’s tours of Zimbabwe and Australia, Hasan picked up four wickets in Worcestershire’s first innings before adding three more in the second.
Kent were bowled out for 238 in their first innings, but Hasan immediately made an impact with the ball, taking two wickets in two consecutive deliveries late on the opening day.
He finished with 4-68 as Worcestershire were dismissed for 217, handing Kent a 21-run first-innings lead.
Kent strengthened their position by posting 358 in their second innings.
Sam Northeast led the way with 132, while Zak Crawley scored 54, Daniel Bell-Drummond made 44 and Chris Benjamin added 36. Hasan contributed six runs after remaining unbeaten on four in the first innings.
Set a target of 380, Worcestershire lost three wickets for just 39 runs before Adam Hose and Brett D’Oliveira mounted a recovery.
Hasan broke the partnership by trapping Hose lbw for 38.
He struck again to dismiss Henry Cullen for 45 before claiming the wicket of Ben Allison to finish with 3-51 in the second innings.
Keith Dudgeon and Matt Milnes also took three wickets each as Worcestershire were bowled out for 295 despite D’Oliveira’s century, sealing Kent’s 84-run victory.
Hasan’s match figures of seven wickets capped another outstanding performance in his County Championship campaign.