Cardiff boss Malky Mackay praised his players for their "resilience" as they to claim their first Premier League away win of the season.
Steven Caulker's early header had been cancelled out by Fulham midfielder Bryan Ruiz just before half-time.
But at the end of the game, substitute Jordan Mutch opened his goal account for Cardiff with a spectacular winner, much to Mackay's delight.
"Any win in this league means a lot and an away win means even more," he said.
"But I thought we thoroughly deserved it, we had 24 attempts on their goal and I thought over the whole course of the game played very, very well.
"We dominated a lot of the ball in the first half and had real good chances, and were really unlucky to go in 1-1 at half-time - it was a fantastic wonder strike from Ruiz.
"But we talked to them about just being resilient and making sure we came out with the same belief in the second half and we did that."
The last time Cardiff were in the top flight was the 1961-62 season, with their last away win at that level also coming at Craven Cottage.
With their performance at Fulham, the current crop suggested that there will be more successes on the road this campaign.
"We kept striving for the win. We put on three substitutions to try to win the game and one of the players [Mutch] ended up scoring a fantastic goal," Mackay added.
"I think we got our just rewards in the end. We deserved to win the game.
"We've got a real belief after six games, about our ability to play at this level and be at home at this level."
The Bluebirds are back in the Cardiff City Stadium next Saturday when Newcastle United are their opponents.