United took the lead in the ninth minute when Wayne Rooney converted his penalty after Chancel Mbemba was adjudged to have handles in the area.
Rooney then turned provider for Jesse Lingard as the Red Devils went 2-0 up seven minutes before half-time.
However, the hosts pulled one back through Georginio Wijnaldum shortly before the break to give Steve McLaren’s men hope.
Aleksandar Mitrovic then scored his penalty after Chris Smalling bundled the Serb down in the box in the 67th minute.
Rooney looked to have secured all three points when he fired into the top corner in the 79th minute.
But the Magpies earned a point thanks to Paul Dummett’s late strike, which deflected in off Smalling.
Speaking on BT Sport after the final whistle, Scholes said: “It was a great game to watch.
“I think United will probably be the most disappointed team, blowing a 2-0 lead and a 3-2 lead as well.
“I think Wayne Rooney was sensational and you have to say Wijnaldum was sensational for Newcastle as well.”
He added: “It’s not a great result but it’s not a bad result. It was the type of football we want to see.”
The result left United sixth in the Premier League table.
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