Magoffin removed all of the top order, including opener Marcus Trescothick for 20, on his way to figures of eight for 20 from 11 overs.
Chris Jordan claimed the other two wickets, while Jos Buttler was the top scorer with 22 on a dismal morning for the visitors. Sussex began their reply before the interval and had reached 13 without loss by lunch.
Division One leaders Middlesex found the going tough at Chester-Le-Street, where hosts Durham were 100 for one at the end of the morning session.
Things looked promising for Middlesex when Mark Stoneman fell to Corey Collymore with just seven runs on the board, but Scott Borthwick (46 not out) and Keaton Jennings (36no) soon got the runs flowing.