The pair took 19 wickets - Mushtaq taking five in each innings - as Sussex won the match by an innings and 39 runs inside five sessions.
Durham had looked to be repairing some of the damage from their first innings total of 110 as they reached 47-0 trying to pass Sussex' first innings total of 229 and set a daunting target for the visitors.
However the peerless Mushtaq shattered their fragile morale by breaking the opening partnership and from then on they met little resistance.
The only positive thing to come from the game was the bowling performance by England paceman Steve Harmison, who showed he will be raring to go for the test series with Pakistan or even the final test with Sri Lanka.
The 27-year-old, who has just returned to frontline action after several months absence with a shin injury suffered two months ago on the tour of India, took 4-19 in 11 overs but in the end his performance paled into insignificance set aside those of Sussex' duo.