Sussex took just 56 minutes to complete an eight-wicket win over Somerset on day four of their County Championship clash on Saturday.
Chris Nash and Ed Joyce had set the hosts on course for their third successive win with a first-wicket stand of 201 on Day three at Hove, after Sussex had been set 272 to win.
Nash, who started the day on 111, moved to 120 from 174 balls before he fell to a Steve Kirby delivery that kept low and hit his off stump.
Sussex whittled away at their target under cloud cover that provided some encouragement for the Somerset seamers.
Goodwin wrapped things up for the home side, first driving Gemaal Hussain through the covers on successive deliveries and then twice giving Willoughby the same treatment to overhaul the visitors.
Victory over the pre-season title favourites saw Sussex move into the top half of the first division table.
A long-awaited hundred for Chris Nash helped put Sussex in sight of an excellent victory over Division One rivals Somerset at Hove.
Opener Nash registered the 10th ton of his career having passed 50 six times already this season. He reached the close unbeaten on 111 as the hosts reached 218-1 in pursuit of a victory target of 272.
Ed Joyce had helped put on a double-century stand for the first wicket and although he fell for 84 late in the day, going lbw to Lewis Gregory, Sussex will return on the final day needing only a further 54.
Somerset have only themselves to blame for their predicament after suffering a batting collapse for the second time in the contest.
They lost heir last seven wickets for 38 in 18 overs either side of lunch to be bowled out for 235 - they had resumed in the morning on 114-1.
Skipper Marcus Trescothick top-scored with 79 - his second half-century of the match - but Nick Compton was the only one of his team-mates to really prosper, making 44 before becoming the fourth wicket to go down.
Rana Naved-ul-Hasan claimed 5-82, including 4-12 in the space of 32 balls, to finish with match figures of 10-161; it is the second time he has taken 10 wickets in a match during his five years with Sussex.
Somerset closed day two of their clash with Sussex in a strong position thanks to a a second half-century in the match from Marcus Trescothick.
The visiting skipper was unbeaten on 64 as his side closed on 114-1 in their second innings, giving them a lead of 150 with nine wickets still in hand.
Arul Suppiah helped put on a century stand with his captain and although he fell late on, stumped off the bowling of Monty Panesar, Sussex had by then surrendered the advantage they had gained on the opening day.
Replying to Somerset's total of 213, the hosts lost six wickets for 24 runs in the space of just six overs after lunch on their way to being bowled out for 177.
It would have been far, far less had it not been for a maiden half-century from James Anyon. He hit eight boundaries in his 82-ball knock before slicing Peter Trego, who 4-24, to cover - to be last man out for 51.
Monty Panesar (14) had helped put on exactly 50 for the ninth wicket after coming to the crease at 95-8, Matt Prior amongst those to fall cheaply as he managed just a single during his six-ball stay out in the middle.
Skipper Marcus Trescothick made 63 but his departure triggered a Somerset batting collapse on a weather-hit day one against Sussex.
Left-hander Trescothick shared in an opening stand worth 71 with Arul Suppiah, who contributed 31 before being trapped lbw by James Anyon.
Still, the visitors had moved on to 117-1 at Hove by the time they lost their skipper, Amjad Khan getting the former England batsman caught by Ed Joyce.
Trescothick was the first of five wickets to go down for just 33 runs, with Rana Naved-ul-Hasan dismissing Nick Compton (19) and Peter Trego (0) in the space of three deliveries.
Jos Buttler became Khan's second victim, adjudged lbw, having made just eight, while all-rounder Lewis Gregory was bowled by Anyon for 10 to leave Somerset reeling at 150-6.
Craig Meschede (18) helped put on 47 for the seventh wicket before he too departed late one, leaving Alex Barrow unbeaten on 37 when play was halted after only 50.1 overs.