Wes Brown was the unlikely scorer of United's first when he leapt to head in Wayne Rooney's cross and the visitors ended the first half with 10 men after Javier Mascherano was sent off for a second bookable offence after arguing with referee Steve Bennett.
Liverpool failed to make a period of second-half pressure tell, and Cristiano Ronaldo headed home the second from a corner in the 79th minute before Nani added a third two minutes later after good interplay with Rooney
Ferguson was hugely pleased with the display and told Sky Sports: "It was a really good performance - a performance of maturity.
"We've seen a team mature over the last six months and today they hit their high peak."
Asked to comment on the dismissal of Mascherano, the Scot added: "He has been booked and kept badgering the referee. We've talked about dissent and I think that was dissent."