The Reds, who knocked Manchester City out of the Carling Cup in midweek, claimed another notable scalp thanks to goals by Daniel Agger and Dirk Kuyt, with Park Ji-sung replying for the visitors.
Much was made in the build-up to the match about the responsibility of both players and fans to show restraint in the first meeting between the two sides since their stormy league encounter in October.
Patrice Evra, who was involved in an altercation with Liverpool's Luis Suarez in that match that subsequently resulted in an eight-match ban for the Uruguayan, was predictably booed by the Anfield support but in their conduct otherwise never crossed the line.
The same was true of the players, with just one booking in an even-tempered match, and Gerrard praised the fans for creating the right atmosphere.
"I thought the Liverpool fans were superb today [Saturday]," Gerrard told ITV1.
"They never let us down and they played a part today [Saturday]. They pushed us through.
"They realised we were very tired after midweek, but when they're pushing they suck goals in, and I think they sucked Dirk's goal in today [Saturday]."
Gerrard conceded, however, that United had dominated much of the game before Kuyt struck the winner in the 88th minute.
"We've got to give Manchester United credit," he said.
"They controlled large parts of the game but the most important thing was the result and we got there in the end.
"We had a tough match in the week so you've got to give the team credit for all the effort and commitment for the way we played today [Saturday]."