Former Pakistan leg-spinner Mushtaq recorded 200 first-class wickets for Sussex, taking eight in the match in all, as the south coast club won their first championship match of the season.
Warwickshire, who lost by an innings and 87 runs, had not been beaten in the championship since their final match of 2003.
Mushtaq, whose 84 wickets last season was 12 more than any other bowler in the country, followed up his four for 73 by taking four for 65 in Warwickshire's second innings.
The champions resumed on 141 for five in reply to Sussex's 412 and, after being forced to follow on 233 behind, the visitors were bowled out for 146 on the stroke of tea.
At Canterbury, Simon Katich took over from where his Australia team-mate Shane Warne left off as Hampshire built a strong position on the second day of their match against Kent.
Just 24 hours after Hampshire skipper Warne struck his maiden first-class hundred in the visitors 328, Test batsman Katich posted an unbeaten 125 - including six sixes and six fours.
That helped Hampshire finish the day on 191 for two in their second innings, a lead of 214.
Earlier, Kent were bowled out for 305 with leg-spin great Warne and seamer Richard Logan each taking three wickets.