Amini got things going for AGF, netting a low drive volley in the 21st minute for the Denmark club, with the Socceroos hopefuls were in the thick of the action throughout the contest.
Lazio loanee, Ikonomidis, played the entire match for the 11th-placed AGF and picked up a yellow card in the 95th minute.
Unfortunately for AGF though, they conceded a late penalty as the last-placed Viborg drew level in the 88th minute.
Amini, who has now scored five goals in 23 appearances this season, recently told The World Game he hasn't given up hope in securing a place in the Socceroos squad ahead of the upcoming crucial 2018 FIFA World Cup qualifiers.
"It's a big year for the Socceroos with World Cup qualifiers and the Confederations Cup," Amini said.
"Things can change fast in football, so you never know. You just have to keep working hard and waiting."
Elsewhere in Denmark, former Adelaide United attacker Awer Mabil played the full 90 minutes, alongside fellow Australian Brent McGrath, in 12th-placed Esbjerg's 0-0 draw away to high-flying Lyngby.
Mabil has been in outstanding form for Esbjerg and scored a goal and two assists in last round's 3-0 win over SoenderjyskE.
