A 1-0 loss to West Bromwich Albion on Saturday left United still in fourth place but only four points ahead of Liverpool with three Premier League games to go.
Liverpool relied on Steven Gerrard's late goal after the captain missed a penalty, to beat 10-man Queens Park Rangers 2-1 at Anfield.
United's slump has come just when it appeared to have turned a corner under Louis van Gaal, reeling off six successive victories before this latest downturn at Old Trafford.
"We knew in defence they park the bus so we have to deal with that, and in the first half we didn't create enough chances to score," Van Gaal said. "The finishing was not good enough."
West Brom, though, will be more hopeful of surviving in the topflight after Chris Brunt's free kick was deflected into the net by Jonas Olsson in the second half, and United striker Robin van Persie then had a penalty saved.
The central England team is seven points clear of the drop zone. But Newcastle has been sucked into a relegation battle by losing a club record eight Premier League games in a row.
As if the club wasn't in enough disarray after a 3-0 loss at Leicester, manager John Carver then accused one of the two dismissed Newcastle players of intentionally getting sent off.
Discussing Mike Williamson's late knee-high challenge on Jamie Vardy after an hour, Carver said: "I thought he meant that and I have told him so."
Newcastle was already losing at that point, having conceded two goals from Leonardo Ulloa and another from Wes Morgan.
Leicester is a point and a place above the danger zone but relegation rivals have games in hand, including Sunderland, which is directly below them. Jordi Gomez scored two penalties to clinch a 2-1 victory over Southampton, of which Jamie Ward-Prowse was sent off.
Aston Villa edged Everton 3-2 to stay two points clear of Sunderland, with Christian Benteke scoring twice and Tom Cleverley adding a third for the FA Cup finalists.
But Burnley and QPR nudged closer to an instant return to the League Championship after losses.
Burnley is eight points from safety — with nine points to play for — after Mark Noble converted a penalty following Michael Duff's sending off to give West Ham a 1-0 victory.
QPR is a point above Burnley. Although Leroy Fer volleyed QPR level at Anfield, cancelling out Philippe Coutinho's first-half opener, the London club saw Nedum Onuoha sent off 10 minutes later for fouling Jordon Ibe before Gerrard's winner.
There was only one match in the Premier League with few nerves on Saturday. Swansea beat Stoke 2-0 in a mid-table clash, and the eighth-place side is set for its highest ever finish.
The day's football began with Bournemouth being promoted to the Premier League for the first time as second-tier champion after Watford threw away the title in the final seconds of the season.
Already guaranteed promotion, Watford led the League Championship heading into Saturday's final round and was beating Sheffield Wednesday 1-0 until stoppage time when it conceded to draw 1-1.
That meant Bournemouth clinched the trophy by a single point by beating Charlton 3-0, only five years after the south-coast team was playing in the fourth tier.
There is another spot in the Premier League available to the playoff final winners. In the two-leg playoff semifinals, Norwich will play Ipswich in an east coast derby, and Middlesbrough will face Brentford.
The season ended in controversy for last-place Blackpool, with a protest by fans against chairman Karl Oyston leading to the game against Huddersfield being abandoned. Three minutes into the second half hundreds of disgruntled Blackpool fans poured onto the field, forcing the referee to take players off.
The Football League said it will decide whether to replay the match, but Blackpool had already been relegated and also faces Football Association action over its fans' behaviour.