Pajtim Kasami headed home a Damien Duff corner five minutes into the second half to snatch the points in a 1-0 win in what was the visitors' only clear chance of the match.
But despite their evident relief at securing an unlikely victory, both Hughes and Fulham boss Martin Jol insisted much improvement is necessary in order to sustain their early momentum.
Jol admitted: "We have to do better in future to get results. You have to play your football and get out from the back and we didn't do that - but I was very pleased to get the points."
Hughes' rock-solid central defensive partnership with captain Brede Hangeland was the main reason the visitors managed to soak up the waves of attacks by the home side.
Boss Paolo Di Canio started with five of his summer signings and each impressed, with midfielder Cabral twice drilling just wide from long range, and right-back Ondrej Celustka bringing a stunning save out of Maarten Stekelenburg in the first half.
Kasami, a junior Swiss international who spent much of last season on loan at Luzern and only started at the Stadium of Light because Bryan Ruiz was jet-lagged after international duty, stole the show with the simplest of headers.
Hughes told Fulham's official website: "It wasn't vintage from us and I wouldn't put it down as one of our best performances but in terms of being resolute and strong and showing lots of character it is up there.
"To come up here in the first game of the season and come away with the three points is a big achievement. It's a confidence-booster for us and we look forward to doing it again next week."
Di Canio cut an increasingly frustrated figure on the touchline as his side did everything but discover the crucial cutting edge.
His new boys bedded in quicker than might have been expected, with Cabral and Celustka particularly impressing and Emanuele Giaccherini linking up well with Jack Colback down the left.
But clear chances went begging up front for Jozy Altidore, who was fresh from a midweek hat-trick for the United States but was twice denied at close-range, first by a Duff interception then by a brave save by Stekelenburg.
Altidore came closest to an equaliser in the 65th minute when he was picked out by John O'Shea in the box and swivelled past Hughes before firing narrowly wide of target.
Altidore admitted on Sunderland's official website: "We just have to do better mentally at not giving away the game. It's difficult but also we have to create even more chances.
"This is the best league in the world and that's why it can be so cruel but at the same time we have to take the positives away and look forward to the next match and try to get some points."
Sunderland's last chance to claim a share of the points fell to Ji Dong-won in final minute of normal time, but the South Korean substitute headed a fine chance wide.
Fulham's celebrations were dampened by injuries to Kieran Richardson, who hobbled off after 19 minutes with a hamstring complaint, and new keeper Stekelenburg.
The Dutchman suffered a shoulder injury when saving from Altidore in the 75th minute and had to be replaced. Although tests did not show a dislocation, the injury is likely to keep Stekelenburg out for the rest of the month.