Former Zimbabwe batsman Goodwin, acting captain in place of the injured Chris Adams, led from the front as Sussex finished on 399 for seven, a lead of 60, when bad light forced an early close.
Sussex had been on the backfoot ever since being bowled out for 200 on the first day.
They then saw Essex wicketkeeper James Foster advance his case for an England recall by making an unbeaten 110 in MCC's 539 for eight declared. MCC skipper Andy Flower, a former Zimbabwe teammate of Goodwin's and like him now retired from international cricket, made 76.
Sussex were still 124 behind come the start of Monday's play with Goodwin, who also plays first class cricket for Western Australia, unbeaten on 43.
He went to his 28th first-class hundred in 140 balls including one six and 18 fours. But two balls later he was caught by Alistair Cook off the medium pace bowling of England 'A' captain Alex Gidman.