Kick-off was delayed by half an hour as the United team bus fell foul of London traffic but it took a good deal longer for much excitement to arrive, as White Hart Lane endured a dour first half without a shot on target.
But 0-0 became 3-0 within six scintillating second-half minutes as Dele Alli, Toby Alderweireld and Erik Lamela struck to land damaging blows against United's hopes of a top-four finish.
Tottenham's outlook is comparatively more positive after they eventually found an impressive response to Leicester's earlier win at Sunderland to sit seven points behind the leaders with five matches remaining.
United lie fifth, four points shy of neighbours Manchester City, and contributed little as an attacking force in the latest turgid showing of the Louis van Gaal era.
This result, combined with Leicester's 2-0 success at the Stadium of Light, means Claudio Ranieri's men are now assured of Champions League qualification for next season.
Playing for the first time since suffering medial knee ligament damage in January, Jan Vertonghen made an important challenge to stop Anthony Martial's mazy run as United started brightly despite their delayed arrival.
A rare handling error from United goalkeeper David de Gea forced Timothy Fosu-Mensah, preferred at right-back to Matteo Darmian, into a last-ditch challenge on Harry Kane with the goal gaping.
The visitors failed to fully clear the danger and Christian Eriksen's right-wing cross to the recalled Lamela at the back post deserved better than a woeful headed miss.
A lack of service meant Marcus Rashford was hardly the main culprit in United's first-half struggles but the teenage striker was replaced by Ashley Young, who took up a central attacking role after almost three months out with a groin injury.
De Gea punched clear as Eriksen fired goalwards from the left wing before having his palms warmed by Eric Dier and Kane.
Young's introduction as an unlikely attacking spearhead had done little to increase United's potency but Martial almost opened the scoring in the 62nd minute.
The France forward glided in from the left past a clutch of Spurs defenders but thumped his eventual shot too close to goalkeeper Hugo Lloris.
De Gea reacted well to clear Danny Rose's deflected cross with his right boot, while a selfless tackling display from Fosu-Mensah came to a close in the 68th minute as he limped off to be replaced by Darmian.
The opening goal arrived from the Italian's flank shortly afterwards – Eriksen scampering forward following a scrappy passage of midfield play and his first-time cross was matched by an instant finish for Alli's eighth league goal of the season.
United's impressive discipline deserted them entirely as Alderweireld powered home Lamela's free-kick.
Darmian was booked for a foul on Kane to bring about that opportunity and a dismal cameo continued as he watched Rose spear a low cross past him for Lamela to sweep home emphatically in the 76th minute.
De Gea tipped over Kane's header as a rampant Spurs underlined their credentials, while United must regroup quickly for Thursday morning's (AEDT) FA Cup sixth-round replay at West Ham.
United lie four points behind fourth-placed Manchester City having ceded the ground they gained by winning last month's Manchester derby.
"Every team can lose to everybody so still we are in the race, but of course when you lose a game you have to close the gap again and that's more difficult," Van Gaal told Sky Sports.
"I think that Tottenham is a great team and I've said that also in advance of this match. Until the first goal we were the better team and also had a big chance for the first goal.
"To lose by three goals is a big negative result but the way that we have played until the first goal was good."
Alli continued his superb breakthrough season by scoring an eighth Premier League goal this term, the day before his 20th birthday.
The England international told Sky: "It's important that we keep winning games and finish the season strongly on a good run.
"They were never going to make it easy for us but we knew the chances would come if we were patient.
"My target was to get to 10 this season but I'll take eight."
Alli added: "It's important we don't get too focused on the league. We've had a great season together as a team and whatever happens it's been a great year for us."
