A draw at Manchester City and a win over Chelsea preceded last weekend's vital 4-0 triumph for Sunderland against Cardiff and Gus Poyet's men made it 10 points from the last 12 on offer thanks to Sebastian Larsson's first-half volley.
Defeats to Stoke City and Newcastle United respectively meant Fulham and Cardiff's fates were sealed, while Emanuele Giaccherini and Fabio Borini both hit the United woodwork in the closing stages.
Sunderland now hold a three-point lead over third-bottom Norwich City - who take on Chelsea on Sunday in their penultimate game - and a vastly superior goal difference.
Following a vibrant 4-0 win over Norwich last Sunday, interim United manager Ryan Giggs crashed back down to earth as a lacklustre display that allowed the visitors to claim a first league win at Old Trafford since May 1968.
A combination of illness and a minor groin injury kept Wayne Rooney on the sidelines - the only enforced change of five made by Giggs to his starting XI.
Former United defender John O'Shea almost turned Michael Carrick's 16th-minute cross into his own goal, while Nani fizzed over and Patrice Evra headed a 20th-minute corner into Vito Mannone's arms - though clear-cut chances were at a premium.
However, United's early lethargy remained and the travelling supporters were able to enliven a pensive Old Trafford atmosphere when Sunderland took a 30th-minute lead.
Darren Fletcher allowed in-form striker Connor Wickham to send over a cross from the right and Larsson sent a controlled volley into the bottom-left corner.
Sunderland winger Adam Johnson twice failed to capitalise on poor clearances from goalkeeper David de Gea as United staggered towards the interval in disarray.
United's pedestrian tempo continued after the break but Johnson switched off to allow the overlapping Evra into the box and his 50th-minute centre was superbly cleared behind by Wes Brown with Javier Hernandez poised to convert.
Nemanja Vidic headed wide when the resulting corner was worked back into the area and Sunderland suddenly found themselves defending perilously deep.
Activity in front of the away team's goal became somewhat frantic and Carrick and Vidic were both unable to force headers home when Phil Jones chipped towards the back post.
Sunderland almost made the points safe on an increasingly rare foray forward after 71 minutes - substitute Giaccherini hitting the post before Jack Colback crashed the rebound into the side netting.
By that stage, Giggs had also called for considerable reinforcements in the form of Adnan Januzaj, Danny Welbeck and Robin van Persie and the latter almost enjoyed a dream return from his knee injury but prodded wide from Jones' delivery.
Fellow striker Hernandez skied over from Evra's 81st minute cutback before Borini came agonisingly close to compounding United's misery, striking the woodwork with De Gea rooted to the spot.
Reports this week suggested Van Persie's countryman Louis van Gaal is the front-runner to become David Moyes' permanent successor at Old Trafford and he may have a major overhaul on his hands on this evidence.
