Now Quins await the winners of the final tie between two former Heineken Cup winners, Brive and Munster, after joining two more French giants in the semi-finals, Stade Francais Paris and ASM Clermont Auvergne.
"There are some amazing teams left in this competition and it's like being in the Heineken Cup. That's how we are viewing it," said Evans.
"We are really looking forward to playing whoever we meet - Brive in France or Munster at the cauldron that is Thomond Park in Limerick. It is always really satisfying when a team wins a quarter-final, but we know we will have to play better as we move on.
"We had a fast start, but we slipped off after that. But we managed to stay ahead and play some good rugby and in the end it was enough.
"I was pleased to be back in the groove with my goalkicking after missing a few against Leicester last week. I was disappointed at that, but it was nice to have my rhythm back tonight."
Quins director of rugby Conor O'Shea warned his players they will have to improve on their quarter-final performance if they are to stay on course for a third Challenge Cup final in Cardiff on Friday, May 20.
"We were far from perfect, but we've played better than that this season and lost. This is a great competition and, whoever we play in the next round, it will be a fantastic learning curve for our younger players," said O'Shea.
"We know we will have to improve defensively, but we won't be going to France or Ireland merely to make up the numbers."