The Manchester United striker sensationally beat Adrian with a volley from just inside the opposition half in a comfortable 2-0 victory at Upton Park for David Moyes' side.
The 28-year-old found the net twice as United beat West Ham 2-0 at Upton Park, with his first a goal-of-the-season contender.
Rooney caught West Ham goalkeeper Adrian off guard in the eighth minute to score with a superb half-volley from more than 50 yards.
The goal prompted inevitable comparisons with former United winger David Beckham's famous strike from the halfway line against Wimbledon in 1996.
Beckham was in attendance at Upton Park on Saturday, with the ex-England captain allowing himself a wry smile at Rooney's effort while watching from the stands.
Speaking to Sky Sports, Rooney said: "It's just instinct, I've turned, had a look and seen him [Adrian] off his line.
"I've tried it many times and thankfully today it's gone in. I wouldn't say it's my favorite. They're ones you try in training, they don't always come off, so when they do it's great and great to put us in that position.
"I think the Olympiakos result was massive in terms of picking the fans up and picking ourselves up. Today we played some lovely football and we're disappointed we didn't take more chances."
Having lost 3-0 to rival Liverpool last weekend, United now faces another derby against Manchester City on Tuesday.
Rooney feels that United can face Manuel Pellegrini's men with renewed optimism after bouncing back from the Liverpool defeat with successive victories.
He added: "Today was a good result, a much-needed result after last week. The win against Olympiakos has given us a big lift. You can see the confidence in the team.
"It's [the City match] a massive game. It's a big game for the city, the fans and the players. We're looking forward to a big challenge. We go into the game confident after the last two results."