It took the visitors just 22 minutes to polish off the last three wickets as Somerset were bowled out for 209 in their second innings, Magoffin taking two of them for figures of four for 36.
That gave the 33-year-old Queenslander match figures of eight for 101 to follow the amazing 12 for 31 he took in the corresponding game at Horsham in May.
A victory target of 91 was never likely to test Sussex, who eased to victory off 19.4 overs before lunch, Chris Nash leading the way with an unbeaten 61.
Surrey faced more toil in the afternoon as they trailed Nottinghamshire by 182 runs in their bid to avoid an innings defeat at the Kia Oval.
Having resumed on 360 for six, Nottinghamshire were all out for 410 as Samit Patel completed his century. Surrey reached lunch on 30 without loss in their second innings.
Keaton Jennings was unbeaten on 113 as Durham piled up the runs against Derbyshire at Chester-le-Street.
The home side reached lunch on 306 for seven to lead Derbyshire by a massive 446 runs.
An unbeaten century from Adam Voges kept the Middlesex hopes alive against Warwickshire at Uxbridge.
Middlesex started the day on on 177 for four and by the break had reached 278 for eight, still 208 runs in arrears on first innings, with Voges not out on 141.