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.
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.
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.
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.
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.
