Despite their form it could be argued the victory was coming - five of the Dragons' last six Guinness PRO12 matches have been settled by six points or fewer.
Now a semi-final lies in wait against Montpellier, who have notched 27 points from a possible 30 in their last six Top 14 matches.
But Wales No.8 Faletau says his team have proved just how resilient they can be.
"We have still got something to play for," he said. "We have been to France and won some games.
"These are one-off matches, knockouts. We will be working hard on going there and executing our game plan.
"We watched Montpellier beat Sale Sharks. They have got massive, physical men and we have got to try and stop them applying their game. It's possible to win but it will be tough.
"There's relief because we hadn't won a game for a while and, to get a win in a quarter-final away from home was great. You have got to enjoy these moments.
"We will get a lot of confidence from it."
To buy tickets for the Guinness PRO12 Grand Final click here. Also follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the Guinness PRO12.