The visitors did have cover for that eventuality. But when Phil Jones had to be stretchered off following a nasty clash of heads with Jonathan Walters, with Nemanja Vidic suspended and Rio Ferdinand not making the squad, there was none.
It meant Michael Carrick was forced into central defence alongside Chris Smalling in just the game you would not choose to be weakened.
In between the substitutions came another piece of ill fortune for the visitors.
It was debatable whether Adam's long-range free kick was even on target when it struck Carrick on the edge of the box.
Once it had, David de Gea had no chance of keeping it out and the ball rocketed into the far corner, leaving the United 'keeper stranded.
Mata appeared a largely peripheral figure and neither Wayne Rooney nor Van Persie threatened with any regularity.
Van Persie came near with a close-range header that rebounded over off Glenn Whelan.
Rooney had a couple of long-range efforts but with his team struggling to cope with the conditions, it was a surprise Welbeck was introduced for Jones given Antonio Valencia would have allowed Mata to move into a central position, or Darren Fletcher would have kept Rooney in an attacking one.
It took just two second-half minutes for Mata and Van Persie to show what they are capable of.
Marc Wilson's poor clearance from inside his own box offered Mata the chance to turn a perfectly-weighted pass to Van Persie, who lifted a first-time effort over Asmir Begovic and into the corner.
It was the Dutchman's sixth goal in seven Premier League games, split by a thigh injury.
United was soon behind again, with Adam once again the scorer.
This time there was no fortune either as he let fly following a blocked Marko Arnautovic shot, sending his 25-yard strike arrowing into the corner.
