Amini sent the away fans into raptures with an incredible curling effort 10 minutes from full-time to give AGF Aarhus a 2-1 victory over Odense Boldklub in the Danish Superliga.
The long-range strike was the 26-year-old's first of the season and was enough to send AGF third, eight points behind Awer Mabil's Midtjylland, who play FC Copenhagen on Monday.
With Zach Duncan a second-half substitute, manager David Nielsen also brought on fellow Australian Alex Gersbach in the dying stages to preserve AGF's slender advantage.
The game time awarded to all three players will have pleased Socceroos coach Graham Arnold, who has made a habit of rewarding merit over experience.
Goodwin meanwhile managed to get his name on the scoresheet for the first time in Saudi Arabia as Al-Wehda won 1-0 over Al-Fayha.
Making his fourth Saudi Professional League appearance since signing from Adelaide United, Goodwin's 78th-minute goal earned the Red Giants their second successive win of the season.
Brad Jones, however, was unable to follow suit in the winner's circle on Saturday, with Al-Nassr going down 1-0 at home to Al-Hazem.
Al-Nassr dominated proceedings in Riyadh but were unable to put the ball past Malik Asselah.
Elsewhere, compatriot Apostolos Giannou had a similar outing for Cypriot side AEK Larnaca, with the 29-year-old unable to make the difference in a 2-2 draw with Olympiakos Nicosia.
