Goodwillie, who was arrested in midweek, was dropped to the bench for the Scottish Premier League encounter.
But the 21-year-old scored in his sixth consecutive SPL match seven minutes after coming on to earn United a deserved three points.
United manager Peter Houston made a number of changes as a result of the alleged disturbance in Glasgow city centre in the early hours of Wednesday morning.
Goodwillie, who was released without charge on Thursday, dropped out along with Barry Douglas, who was listed by United as one of four players they understood to have been involved in the incident. Another, Danny Swanson, was missing from the squad after suffering facial injuries.
Houston felt "let down" by his players following the incident, which led to youth team player Scott Allan being charged with assault to severe injury when he appeared at Glasgow Sheriff Court on Thursday alongside two other men.
But the United boss, who brought in Paul Dixon, Danny Cadamarteri and Johnny Russell and dropped Jon Daly to the bench, would have been heartened with the way his side took control against Accies, despite their struggle to find a breakthrough.
The game almost started badly for the visitors though as Hamilton had the ball in the net inside the first minute, but the assistant referee's flag came to their rescue.
Marco Paixao had slid in to rob Keith Watson as the United full-back tried to shepherd the ball out, and crossed for Dougie Imrie to head home just as Calum Murray blew for a goal-kick. The Hamilton forwards protested against the borderline decision, given from 50 yards away.
Paixao, in for Nigel Hasselbaink despite the Dutchman's brilliant winner at Motherwell last weekend, and twin Flavio showed some good early touches.
But United soon began to control possession before passing up the first real chance when Scott Robertson sliced wide from 18 yards after space opened up following a throw-in.
United continued to edge play and Sean Dillon and Russell were both presented with headed opportunities but they were far from clear-cut and again Cerny was not troubled.
Goodwillie emerged to warm up around the half-hour mark to cheers from the visiting supporters but there was little else to shout about for the rest of the half.
Goodwillie was told to get stripped as Cadamarteri limped his way through the early stages of the second half but the former Everton forward recovered to cross well for Prince Buaben, who was narrowly wide with an overhead kick.
The unmarked Russell failed to connect properly with Dixon's deep corner and Accies manager Billy Reid brought in Hasselbaink in a bid to turn the tide. Jim Goodwin departed with Imrie dropping back.
United remained on top though and Morgaro Gomis saw a shot comfortably held after a positive run before the Czech keeper made a more impressive save to catch Buaben's angled drive following Russell's cutback.
Goodwillie eventually came on in the 69th minute as Houston swapped Cadamarteri and Russell for his first-choice partnership of Daly and the Scotland Under-21 player. Hamilton also made a change with Grant Gillespie replacing Mark Mclaughlin.
Daly had an immediate chance when Buaben threaded a pass into his stride but the Irishman could not get enough on the ball to steer it past Cerny.
Accies countered and Flavio Paixao's low drive was held by Dusan Pernis before Cerny gathered Buaben's powerful long-range drive at the second attempt.
The game was growing far more lively and Goodwillie again grabbed the headlines when he netted in the 76th minute.
Martin Canning and David Elebert appeared to get in each other's way as they failed to clear Dixon's deep cross and Goodwillie calmly slotted the ball home from 10 yards.
Hamilton brought on Damian Casalinuovo and he almost netted against his former club with three minutes left when his 18-yard strike crash off the junction off post and bar.