United started poorly as Craig Bellamy cashed in on an error by keeper Steve Harper to score within sixth minutes on his return to St James' Park.
However, Obafemi Martins levelled on 26 minutes with his 12th goal of the season after Jose Reina blasted a clearance into Daniel Agger, and Nolberto Solano won it with a 69th-minute penalty awarded for John Arne Riise's trip on Steven Taylor.
Roeder: "It is always nice to come from behind to win any game, but you do not come from behind very often against Liverpool, especially a Liverpool that is in fine form.
"I would be the first to admit they started better than us and handled the conditions better than us.
"But once we got the lead, the volume, as always at St James' Park, was turned up and the crowd became the 12th man.
"There was no way the boys were going to let the lead slip."