Goals from Ricardo Alvarez and Jordi Gomez, on top of a calamitous own-goal by Fulham goalkeeper Marcus Bettinelli, were enough to earn the Premier League outfit a fifth round clash with Bradford City.
And Poyet was delighted with how his team rallied in the second half, having trailed by a solitary goal at the break.
"We played well in the first half, really aggressive and high, but they scored," the Uruguayan said.
"We were in control and I was happy with our performance in the second half, and I'm happy with the final result.
"Today my players enjoyed playing their football. That was one of the first games this season that I've been really happy, watching my team play."
Despite starting brightly at Loftus Road, the visitors were behind after 28 minutes when Hugo Rodallega capitalised on poor defending to put the hosts ahead.
However, Sunderland's luck changed after the interval when Bettinelli fumbled Patrick van Aanholt's deflected cross into his own net.
Alvarez then bagged a terrific solo effort – his first goal for Sunderland – before Gomez sealed the victory in the closing stages with a well-taken penalty.
