Ashley Young's deflected effort 10 minutes from time ensured United did not follow Liverpool, Arsenal and Chelsea in failing to win their opening match.
Yet on the journey back up the M6, Sir Alex Ferguson's mind will be full of problems.
Nemanja Vidic and Rio Ferdinand will need to be assessed for the calf and hamstring problems that heralded their second-half departures.
And Ferguson will need to find some confidence for De Gea, in addition to a crash course in dealing with crosses, the Spaniard's inexplicable error in gifting Shane Long an equaliser to Wayne Rooney's 12th-minute opener, setting the seal on what turned his Premier League debut into a personal disaster.
The questions that were asked of De Gea in the wake of last week's Community Shield thriller were all batted back by Ferguson.
After spending so much money on the 20-year-old, clearly, the United boss had to build the youngster's confidence.
However, there are some occasions when no defence is enough. And this was one.
United's defenders, already on edge due to De Gea's failure to impose himself during aerial combat, thought they had kept West Brom at arm's length as Chris Brunt pushed the ball out to Long on the corner of the box.
It took a little shimmy inside Chris Smalling to create the space for Long to let fly with a shot for the far corner.
De Gea had the angle covered. On TV at half-time, Gary Neville described it as "a routine save". Inexplicably, he dived right over the top of it.
As the ball squirmed under his body and hit the net, Ferguson's heart must have sank.
It took him six years to find a replacement when Peter Schmeichel quit in 1999. The spectre will hang over him until such time as De Gea, his present deputy Anders Lindegaard, or anyone else, proves worthy of inheriting Edwin van der Sar's legacy.
As nervousness spread through the United defence like wildfire, Brunt crashed a shot over and De Gea desperately clawed a deflected Soren Tchoyi cross from underneath the bar as West Brom tried to make the most of their unexpected opening.
It had all looked so unlikely too.
Apart from brief flurries from the home side, during which time Tchoyi was a particular handful, United were in complete control.
Ferguson's decision to select Tom Cleverley ahead of Michael Carrick in central midfield had been vindicated by the youngster's mature performance.
Ashley Young's final ball might have been slightly askew but such was the regularity with which he got past Steven Reid that goals appeared inevitable.
Nani wasted two glorious chances to double Rooney's 12th-minute opener, which in itself was an object lesson in simplicity.
The visitors came cruising out of their own half, Young laid a pass into the path of his England team-mate, who calmly stroked home from 20 yards.
Struggling with a calf injury since the opening minutes, Vidic eventually gave way just after half-time.
With Patrice Evra sidelined by a knee problem and Rafael ruled out for 10 weeks after dislocating his shoulder in training, what had appeared such a rosy picture for United had changed completely in a matter of days.
Rooney came agonisingly close to putting a rather healthier gloss on things when he flicked Young's cross narrowly wide.
A more powerful header from the England striker hit Gabriel Tamas at close range.
After Nani's free-kick had bounced straight through the West Brom box, Ferguson introduced record signing Dimitar Berbatov for Danny Welbeck.
The Bulgarian gave the home defence a different kind of problem to solve, although the early signs were encouraging for West Brom as neither Young nor Nani were able to locate the target from long-range.
To compound United's injury problems, Ferdinand limped off with a hamstring injury. Phil Jones was introduced, leaving them with one of the most inexperienced defences Ferguson could have ever had in a Premier League game.
Still the visitors pushed forward. And when Young cut a cross back into the six-yard box, the unfortunate Reid deflected it past Foster.
It was typical United. And though West Brom pushed forward gallantly at the end, the visitors held firm, allowing De Gea to breath again.
PA
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