It took them until the 25th-minute to get their noses in front when skipper Ryan Giggs drilled a low shot past keeper Brad Jones from Nemanja Vidic's pass.
They effectively killed to game off six minutes after the restart when the energetic Ji-Sung Park ran on to Wayne Rooney's reverse pass to thump a second past Jones.
From that point on, it was only a matter of by how many they would win as they cruised to the final whistle with Boro barely managing an attack worthy of the name.
Gareth Southgate: "We have to go to Newcastle now and deal with the atmosphere there.
"For us in some respects, it is possibly the last throw of the dice because we need the momentum of a win there to carry into the last couple of games.
"The reality is, as I have said for a number of weeks, that we have to go to Newcastle and win.
"As a group of players and staff, we have to consign today to history.
"The last two weeks, we have been looking for a miracle, really, to get a result against the two teams we have been up against.
"Now we have realistic opportunities and we have to take them.
"We have got it all to do - but we have known that from probably 10 weeks ago."