The visitors needed a win to keep their fading title hopes alive and it all seemed to be going wrong when Ronaldo put United ahead from the penalty spot.
Liverpool absorbed all United's attacking aspirations in the second half and sealed the game 15 minutes from time.
Vidics' miserable afternoon was complete when he was dismissed for fouling Gerrard - Fabio Aurelio curled home the resulting free-kick from 25 yards.
Late on substitute Andrea Dossena lobbed a fourth and give an impressive Liverpool new hope of overhauling United who are now four points clear at the top, but with a game in hand.
"We knew that we had to win and it was very difficult after conceding one goal but we were still willing to go forward, push and try and we had quality.
"After 30 minutes we were playing better. After we scored our first goal we had confidence so little by little we were controlling the game.
"It will still be very difficult but now we have more options and more confidence that we can beat anyone and we can stay closer.
"The main thing was to get three points today. I'm really proud and really pleased, more for the fans and the club."
United chief Sir Alex Ferguson rued defensive errors, and told the club's official web site, "It’s a hard one to take."
"But at this club it’s always about how you respond to a defeat.
When you lose a game: respond. And that is what we will do.
Ferguson didn’t have any complaints about the Serbian’s sending off. "It looked as if (Gerrard) was clear to have a shot at goal, whether Rio could have got across, I don’t know. I don’t think I could really argue with the decision to be honest. We’d have been looking for a red card if it was against us.
"It was just one of these days, we made uncharacteristic mistakes. In big games you don’t want to be doing that. If you see the consistency over the last two years with our defending, you don’t expect it. Neither did the players. But quite rightly if you win 4-1 at Old Trafford you deserve all the plaudits, you can’t deny Liverpool that.
"But if the league was starting today, you’d take a four-point advantage with a game in hand. The goal difference is narrowed, it’s only five goals now. It was a bad day, but we have to kick on now. It was a bad day in terms of the goals we lost."