Clinical Manchester United increased the pressure on Liverpool manager Brendan Rodgers as they capitalised on some poor defending to run out comfortable victors at Old Trafford.
Rodgers - who dropped struggling goalkeeper Simon Mignolet for Brad Jones - can point to a succession of brilliant saves from United's David De Gea and a controversial second goal from Juan Mata as significant factors in defeat.
This, however, will do little to ease the growing concerns for Rodgers and Liverpool, with the memory of their thrilling 3-0 win here in March - in a sequence that almost took them to their first title in 24 years - seeming an age away.
United captain Wayne Rooney gave them an early lead and Liverpool had every right to feel aggrieved when Mata headed in from a clearly offside position to take the game away from them just before half-time.
Even before United took the lead, De Gea made an important save from Raheem Sterling, denying the England youngster on four occasions as well as producing three vital contributions to stop Liverpool substitute Mario Balotelli getting his first Premier League goal for the club.
Robin van Persie's third for United at the end of a lightning counter-attack only added to Liverpool's pain and gave the scoreline a lopsided look given the amount of work done by De Gea.
United's sixth successive league win continued United's resurgence under manager Louis van Gaal and put Liverpool's decline since they came so close to winning the Premier League into even sharper relief. Liverpool now trail third-placed United by 10 points.
Liverpool's owners, Fenway Sports Group, intend to give Rodgers until the end of the season at least to turn matters around given the credit he still has after last season, but after a miserable Champions League campaign was confirmed by their exit at the group stage following the midweek draw with Basel, these are crucial days for the northern Irishman.