A scrappy game was drifing towards a draw when Kevin De Bruyne's 82nd-minute thunderbolt looked to have won the game for City who began the day nine points behind Liverpool.
Yet for the second time in the match, Newcastle replied quickly as Shelvey curled a shot past Ederson in the 88th minute.
Raheem Sterling had fired City in front in the 22nd minute but their lead lasted only three minutes as Jetro Willems finished off a fine Newcastle move.
Despite enjoying overwhelming territorial superiority, City lacked their usual cutting edge as Newcastle sat deep but De Bruyne's late 25-metre strike which cannoned in off the underside of the crossbar appeared to have sealed it.
Newcastle had other ideas though and grabbed a point to leave City manager Pep Guardiola frustrated.
Should Liverpool beat Brighton & Hove Albion later on Saturday, they will move 11 points clear of the champions.
Steve Bruce's Newcastle moved six points clear of the relegation zone before the later kickoffs.
