Kondwani Mtonga's finish in the 57th minute and Felipe de Castro's strike in stoppage time gave the visiting team their first away win of ISL.
The opening phase saw both teams fighting for possession but Mumbai City began to control possession and take the attack to NorthEast United.
Their best chance came in the 13th minute as Nadong Bhutia took a cross-field ball under control near the six yard area before making a run into the box and cutting it back. The ball rolled between Subhash Singh and Andre Moritz and was cleared by a NorthEast United defender.
The visitors, who were still struggling to string together their first attack, got their best chance in the 17th minute as Koke played in de Castro, who cut the ball back onto his left foot and shot just wide of the far post.
Mumbai City dominated the remainder of the first half but could not find a way through the NorthEast United defence.
The second half began with the entry of Mumbai City's marquee player Freddie Ljungberg replacing Moritz. The first chance, though, fell to the visiting team, as Durga Boro shot just over the bar from close to 30 yards out.
The breakthrough for the visitors came 12 minutes into the half as Koke dinked the ball into the six-yard area to Mtonga, who held off Tiago Ribeiro and beat Subrata Paul to the ball before lifting it over the keeper and into the net.
The hosts made their final change in the 71st minute and Ljungberg went down with a thigh injury moments later, reducing the home side to 10 men.
Things went from bad to worse for Mumbai City as Pavel Cmovs got sent off for a rather unnecessary and rash challenge on James Keene. The red card left Mumbai with only nine players on the pitch.
NorthEast took advantage of the two-man deficit as Keene did well to get the ball through the feet of Mandal cutting it back to Felipe, who dispatched the ball into the top corner in the 92nd minute.
Mumbai City, lying fourth in the table, will next face Chennaiyin FC Oct 28, a team that is yet to drop points in ISL while NorthEast United travel to the national capital as they look for their second away win against the Delhi Dynamos FC October 29.