The veteran assisted the first goal for Stina Blackstenius and scored the second herself to put the Blagult in firm control against the debutants, before Lina Hurtig added number three.
Speaking to the media after the game, Asllani said, "We went in with great determination and aggressiveness. It felt like an eventful match. Fun with goals too!"
Since the group stage was introduced in 1997, Sweden have now progressed from their group at the EUROs in all eight editions, adding the win over Poland to success over Denmark last week.
A draw in their final match against Germany is all the Swedes need to top the group, owing to their better goal difference, but Asllani has ambitions for nothing other than another win.
"It was a good performance by the team, and now it's just about focusing on the next match. We want to win against Germany, we don't want to go in and think that we want a draw."
The only downside for the 35-year-old was that she picked up a yellow card for a foul on Ewa Pajor, after the Polish player looked to have caused the first offence by shirt-pulling. Another booking against Germany will rule Asllani out of the Quarter-final.
Asllani made no secret that she thought she was harshly treated by referee Maria Sole Ferrieri Caputi.
"She (Pajor) pulls me down and it's a clear free-kick that I should have. And then I get a free-kick against me and a yellow card. Completely unbelievable!"
When asked if the booking and potential suspension could impact her, she responded, "You know my playing style. Of course it can affect me.
"I have to think about it. It would be stupid not to think about it. That's what's irritating, because I don't want to go into a match with the knowledge that I can be suspended."
With her 49th international goal and an assist and booking on her 201st cap, it was an eventful afternoon for Asllani, who became the first Blågult player to make 20 UEFA Women's EURO appearances.
"It is special, but right now I’m just thinking about the win. Now we just need to rest and recover and focus on Saturday, but it’s always nice to make history," she concluded.
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