The Red Devils were trailing 1-0 at half-time after Antonio Rudiger put the home side ahead on the 21st minute.
However, Martial fired home from close range in the 55th minute to equalise for Jose Mourinho’s men.
And the French striker then added a second and his team’s winner in the 73rd minute.
But Chelsea FC had the final say when Ross Barkley netted from close range in the 96th minute to earn a point for Maurizio Sarri’s side.
Former Manchester United star Neville was impressed by Martial’s performance on Saturday lunchtime in west London, but he admitted that he wants to see the striker perform in the big games more regularly.
Speaking during Sky Sports‘ live coverage of the game, Neville said: “When I watch United when I’m not working on commentary, he [Martial] drives me crazy.
“You can see what he can do and you want more from him. He can make more runs, better movements and get involved in the game more.
“But he turns up in big matches. You just want him to realise his talent. That’s the big thing.”
Before the game, a draw would have looked like a good result for Manchester United, but the fact that the Red Devils were so close to claiming a victory will make this stalemate harder to accept.
The result left Manchester United seven points behind leaders Chelsea FC after nine games of the new campaign.
The Red Devils will now look to prepare for their home Champions League clash against Juventus on Tuesday night at Old Trafford.
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