United’s luck was out as both Juan Mata and Anthony Martial struck the woodwork inside the first 15 minutes and only a brilliant reflex save from Chelsea keeper Thibaut Courtois stopped Ander Herrera from six yards after the break.
But Chelsea arguably had the best chance to win when Nemanja Matic squandered a threatening counterattack in the second period.
And as United ran out of momentum and ideas – although they were unlucky not to get a penalty when Willian handled – Nemanja Matic missed the best chance of the game when he raced clear, only to shoot hopelessly over the top. De Gea also made an excellent double save to deny Pedro and then Azpilicueta.
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Van Gaal’s future was shrouded in uncertainty after a run of four straight defeats – and while a draw offers minor relief, United were still unable to secure the victory the 64-year-old Dutchman so desperately needs.
Manchester United host Swansea on Saturday, 2 January while Chelsea travel to Crystal Palace on the following day.
Elsewhere, Mesut Ozil inspired Arsenal to reclaim top spot in the Premier League, as they won their first league meeting with Bournemouth.
The in-form playmaker set up the Gunners’ opener for Gabriel Paulista and put his own name on the scoresheet to take the home team past Leicester City in first place
The home side could not add further gloss to a scoreline that ended Bournemouth’s impressive six-match unbeaten run but, unless Leicester City beat Manchester City on Tuesday night, Arsenal will lead the way at the mid point of a thrillingly unpredictable title race.