Rooney took his tally to nine goals from his last six matches and 26 for the season, opening the scoring with a clever volley in the 36th minute and doubling the lead with a clinical 71st-minute penalty at Old Trafford.
The win lifted the champions to 67 points from 28 games, one more than Manchester City who are second after leading the table since the middle of October.
"It was a surprising day for us I suppose, but we needed that performance after the disappointment of Thursday," he told Sky Sports News.
"We played some fantastic football today and we should have scored a lot of goals. The most important thing was the performance and hopefully the goals can come later."
"I am happy to be there because only a few weeks ago we were five, then seven points behind them, now we are one point ahead, so we have turned around eight points and that's credit to the players and shows the resilience of our squad because, as everyone knows, we have had a lot of injuries," he said.
"For the last 10 minutes of the first half and throughout the second half we had control of the game and should have scored," he told Sky.
"But we did not score and made a mistake at the end to concede a goal. We had the chances but we needed to score and if you don't score, like against Sporting and now for two games, well, clearly, it's a problem.
"We might be in a difficult moment now, but there are still 10 games to go."
City could have fallen behind in the seventh minute when Joe Hart conceded a penalty after bringing down Wayne Routledge before redeeming himself by saving Scott Sinclair's spot-kick.
Luke Moore, who had been on the field for four minutes after replacing Danny Graham, found himself unmarked in space and this time Hart was powerless to stop the effort, following Routledge's perfect cross.
