The highly-rated Amini, who struggled for first team opportunities during a frustrating past three years at Borussia Dortmund, has quickly set about making up for lost time since joining the Danish Superliga club in June.
The 22 year-old midfielder provided an assist in the club's 1-1 draw with top flight Swedish team Hacken FC in his debut match and backed that up with another one in the first leg of qualifying against the Andorran club on Friday 3 July.
He continued to endear himself to his new club with an impressive second leg goal helped his team through to the second round of UEL qualifying.
The Australia Under-23 international expressed his delight on social media.
Reflecting on his stellar start to life at Randers, Amini said: "I am feeling better and stronger every day and hopefully it's beginning to show in the way I am settling in here.
"Of course, I am still getting get into the swing of things and being at a new club, it always takes time ... but so far so good for me.
"We've now earned a tie against the Swedish champions Elfsborg in the enxt round of the Europa and that's going to be a really good test for us.
"The first leg is next Thursday and I can't wait for that. Then we have our first league game against (Danish champion) FC Copenhagan on the weekend after that and it's good to be playing at this level.
"It was great to get on the scoresheet. Any midfielder will tell you that chipping in with goals is an important pat of our role and I was happy with that. Mine was the opening goal for us, which was important and helped set us on our way."
Amini's career had stalled since leaving Central Coast Mariners for Dortmund in 2012. After inking a four-year deal with the Bundesliga club in 2011, Amini was loaned back to the Mariners the next year, playing a starring role in the Premiership win.
He wasn't able to replicate that form in a star-studded Dortmund outfit, despite earning public praise from then-coach Jurgan Klopp.
Having seemingly resurrrected his career in Denmark, the player regarded as one of Australia's brightest midfield prospects hopes to press his claims for Socceroos selection.
"I just want to keep going now ... and if I can keep going in this way then maybe I can get looked at for the Socceroos in the qualifiers we have coming up for the World Cup," Amini said.
"That's always been a massive goal of mine - and now more so than ever.
"There's also the Olympic Games coming in 2016 and being a part of the Olyroos squad is also huge for me right now.
