City boss Pep Guardiola must have thought his side had won it when Kevin de Bruyne found the net in the 82nd minute with a brilliant long-range effort which went in off the crossbar.
But with two minutes of normal time remaining, home substitute Christian Atsu pulled the ball back for Shelvey, who beat the dive of Ederson.
Guardiola’s side have now dropped 13 points this season and are 11 behind leaders Liverpool.
It all began well for City when they took the lead after an early period of dominance.
David Silva, sorely missed by the champions in their recent defeat by Liverpool, highlighted his worth with a deft backheel to find Raheem Sterling, who curled in for his 15th goal this season.
However, before City could assert their dominance, the Magpies equalised through full-back Jetro Willems, who received a square pass from Miguel Almiron before calmly slotting home.
That was the Dutch loan signing’s second goal of the season and the eighth Magpies goal in the past 10 scored by a defender.
City’s Gabriel Jesus and De Bruyne were thwarted by Martin Dubravka after the break before substitute Bernardo Silva pulled a shot wide from eight yards. In stoppage time, Sterling’s shot from six yards lacked venom and allowed Dubravka to make an easy save.
Up next for Guardiola’s side is a trip to Burnley, and they cannot afford any more slip-ups.
