NorthEast nearly scored the winner in the dying minutes but substitute Khassa Camara's long-range strike missed the crossbar by inches.
Aniket Jadhav's strike (53rd minute) was the difference between the two sides in what was the 500th game of the ISL.
Idrissa Sylla (40th-minute penalty) scored the opening goal before Igor Angulo (43rd) equalised just before the break.
The draw ensured that NorthEast United FC remained unbeaten after two games.
ISL 2020-21: Gerard Nus' NorthEast United put up inspired performance to spoil start of Mumbai City's mega project
Ahmed Jahouh's sending off gave a helping hand to NorthEast United in their win over Mumbai City but Gerard Nus' side also impressed with its tactical versatility, disciplined football, and a fearless attitude.
A red card to Jahouh and a penalty turned the game, that Mumbai were otherwise dominating, on its head and handed NorthEast United FC a winning start
A new season brings new hope. Under Spaniard Gerard Nus, NorthEast United FC will aim to find some consistency after a difficult last season.
Ghana Football Association fires all coaches on payroll, including men's and women's senior teams, without reason
The Ghana Football Association has fired all its national team coaches in a drastic and unexpected move.
In a dramatic turn of events, just before a crucial match against Portugal, Ghana have indefinitely suspended two of it's stars - Sulley Muntari and Kevin-Prince Boateng.