0305 GMT January 20, 2020
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, BBC Sport reported.
But with two minutes of normal time remaining substitute Christian Atsu pulled the ball back for his teammate Shelvey, who beat the dive of Ederson with his strike.
That is now 13 points dropped by Pep Guardiola's side.
It all began well for City when it took the lead after an early period of dominance.
David Silva, sorely missed by the champion in its recent defeat against Liverpool, highlighted his worth with a deft back-heel to find Raheem Sterling, who curled in for his 14th goal this season.
However, before City could assert its dominance the Magpies equalized through fullback Jetro Willems, who received a square pass from Miguel Almiron before calmly slotting past the Brazilian keeper.
That was the Dutch loan signing's second of the season and the eighth Magpies goal in the last 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. And in stoppage time Sterling's shot from six yards lacked venom which allowed Dubravka to make an easy save.
Up next is a trip to Burnley for Guardiola's side, which now cannot afford any more slipups.