The England and United skipper was perfectly placed to hook a powerful volley past keeper Simon Mignolet after 78 minutes when a header from Marouane Fellaini bounced off the crossbar.
Rooney has now scored in four successive games and took his Premier League tally to 176, more than any other player for one club, overtaking the previous record of 175 that Thierry Henry managed for Arsenal.
Liverpool-born Rooney, who began his career at Everton, said he was going to relish the thought of scoring at Anfield, something he had not done for more than decade.
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"It was massive victory for us," he told Sky Sports "and continues our good start to this year. I didn't know about the record, but that's not what I'm feeling now.
"To score the winning goal at Anfield, that's a long time for me since my first year at United, so I'm going to be a bit selfish and enjoy that the most."
The victory lifted United back up from sixth to fifth place in the table, two points behind fourth-placed Tottenham Hotspur, while Liverpool remained ninth with 31 points.
Despite the great heritage of two clubs who have won 38 English titles between them, the latest clash lacked the intensity of some of their titanic battles of the past.
There was little of note in a scrappy first half in which United failed to create any scoring chances and although Liverpool did test United goalie David de Gea, none of their attempts posed a real threat.
The match improved a little as a spectacle after the break with De Gea making two important second half saves from Roberto Firmino and Emre Can to keep his side in the game before Rooney struck.
(Reporting by Mike Collett; editing by Martyn Herman)
