But with defending champions Leinster and double winners Munster both going down in round 1 defeats to English opposition, it was left to Ulster to keep the Irish flag flying as they downed fellow former winners Bath 26-12 at Ravenhill last Friday.
Now they will be out to keep that momentum rolling with a trip this weekend to Murrayfield to take on Edinburgh, but they will be wary of a Scottish team wounded by the size of their 31-7 opening round defeat by Stade Francais.
"We have had a good start but we have to keep our feet on the ground because Edinburgh is a place where we always have a tight game," explained Ulster flanker Stephen Ferris.
"They beat us at Ravenhill earlier in the season in the Magners League and the result there always seems to turn on a bounce of the ball or a kick from Chris Paterson.
"They are a dangerous side and we will need to close them down and play some more rugby like we did against Bath. It was a fantastic start for us and. we just need to keep the ball rolling now. Getting the result was the most important thing.
"I saw in the paper that the bookies had us at 100/1 to win the Heineken Cup. That really annoyed me.
"We wanted to prove we are a team on the up and I think we did that. One of our goals is to get out of the group this season.
"Even though Edinburgh beat us at Ravenhill, we can take some encouragement from that game because we created a lot of chances.
"This is a different competition and people up their games for the Heineken Cup."
He added: "I think it's a pretty even group and every side is going to be difficult to beat at home. We are riding on some momentum at the moment and we will look to take that to Edinburgh.
"But we have to stay on an even keel and not get ahead of ourselves - we have won one game, not the Heineken Cup."