Marcus Tavernier’s first-half opener set Chris Wilder’s men on their way to a second consecutive away win before Folarin Balogun doubled the lead soon after the break.
Josh Coburn and Duncan Watmore then jumped off the bench with goals to join the party as Boro moved into the top six in style.
Two teams with very different objectives, but a shared requirement for victory, served up a terrific opening period and the only surprise was it produced just one goal.
That breakthrough went the way of Boro as Tavernier steered a fine strike from the edge of the box past Dai Cornell in the 26th minute.
His third goal of the season arrived after Paddy McNair laid the ball perfectly into his path.
Defender McNair had been Boro’s saviour at the other end moments earlier when racing back to clear an ambitious 50-yard strike from Jack Marriott after keeper Joe Lumley’s dash out of his area backfired.
Lumley redeemed himself with a reaction save from debutant Posh defender Emmanuel Fernandez – a 20-year-old former non-league player – and the Boro number one also denied Jonson Clarke-Harris from point-blank range on the stroke of the interval.
By then Balogun should have doubled the visitors’ advantage when seeing a shot cleared off the line by defender Josh Knight.
That was a second crucial contribution from Knight, who had thrown himself in the way of a goalbound Matt Crooks shot when the contest was still deadlocked.
But Middlesbrough – and indeed Balogun – didn’t have to wait too long to strike again as their second goal arrived only four minutes into the second half when the England Under-21 ace pounced at the back post.
A third goal in his last four Championship outings – following a midweek brace on international duty – provided another example of Balogun’s predatory instincts and highlighted the flaws of the worst defence in the Championship as Knight and Fernandez failed to deal with Jonny Howson’s chipped cross.
Further damage was inflicted by two Boro substitutes late on as they enjoyed an excellent away day while Posh returned to the bottom of the table.
Watmore darted down the left in the 82nd minute and cut into the box to put a tap-in on a plate for fellow replacement Coburn before getting in on the act himself by racing clear and thumping a fine finish past Cornell in the 90th minute.
It was perfect preparation for Boro ahead of a series of crucial clashes against the Championship top three – Fulham, Bournemouth and Huddersfield – this month.
Meanwhile, Posh’s days at this level are surely numbered.