The 36-year-old Australian took his season's tally to 50 wickets for the fifth successive summer but not before Worcestershire had totalled 306.
Skipper Daryl Mitchell (75) and Ben Cox (69) both made half-centuries.
West Indies paceman Miguel Cummins then burst in to take 3-19 to reduce Sussex to 50-4 at the close of play.
On his Worcestershire debut against Essex at Chelmsford last week, bowling largely to Alastair Cook and Tom Westley, Cummins sent down 28 overs and took 0-114.
But after removing Fynn Hudson-Prentice caught behind with the final ball of his first over, he struck again five balls later to clean bowl Craig Cachopa and also trapped Oliver Robinson in the day's final over.
Vice-captain Joe Leach added to his tally of 53 wickets for the season by trapping Chris Nash for 23.
Sussex bowler Steve Magoffin told BBC Sussex:
"Fifty wickets in the season is the benchmark for every new-ball bowler, so to get there for a fifth season in a row is an achievement I am very proud of.
"It's been hard work. At the start of the season wickets were very flat and 50 looked a very long way off. But the coaching staff and the other guys have always been very supportive and in the last month or so it's been nice to get rewards.
"This is a new-ball wicket. Worcestershire bowled very well at us. Once the ball goes soft it does get easy to bat on and we've got players capable of putting partnerships together."
Worcestershire's Ben Cox told BBC Hereford & Worcester:
"It's been a strange day because things have happened in clusters. We lost a couple of early wickets then Daryl Mitchell and Joe Clarke put together a really good partnership before we lost four wickets very quickly.
"My plan after tea was to try to attack Danny Briggs. I just tried to either hit over the top or find the gaps and it worked.
"Getting 306 is a decent effort on that wicket. Then, when we bowled under the lights, it did a bit more off the pitch and Miguel Cummins bowled superbly."
Sussex fast bowler Steve Magoffin claimed a season's best 5-38 at Hove, but could not prevent Worcestershire getting the better of the first day.