Rooney had not played since he suffered a nasty gash on his leg in the club's first home Premier League match of the season against Fulham on August 20.
The England striker failed to get on the scoresheet on Wednesday but his team mates comfortably eased into the next round with goals from Anderson and Tom Cleverley to set up a fourth-round clash against Chelsea.
"It's been just over four weeks since I last played and I'm delighted to be back out on the pitch playing, and it was a good run-out for me and hopefully there's a lot more games to come," Rooney told Sky Sports.
"I feel good, obviously it's always difficult in your first game back after a few weeks but it's great to get the minutes under my belt and hopefully that can benefit me."
United, who are currently second in the Premier League after five games, next play Tottenham Hotspur at home on Saturday.
- Premier League
- Tom Cleverley