The result left second-bottom Boro six points from the safety zone with three matches to play, while City are level with third-placed Liverpool on 66 points and with the same goal difference, a point ahead of local rivals Manchester United.
"I think the fight for the top four will go down to the last game," City manager Pep Guardiola told reporters.
"Everyone who is competing for those places have tough games so it will not be easy but we give absolutely everything in these last few matches to try and be in there.
"It’s a point and we are still there and it now all depends on the final few games at the Etihad,” he said looking ahead to three consecutive home matches in City's remaining four.
Former City striker Alvaro Negredo put Middlesbrough ahead seven minutes before halftime with a shot from the centre of the box that went into the net off the inside of the post.
Sergio Aguero pulled City level in the 69th with a penalty that was hotly disputed by Boro after Marten de Roon was ruled to have brought down substitute Leroy Sane.
The Argentina striker equalled his club record of scoring in five consecutive away league matches.
"From where I was I didn't think that it was a penalty and I thought Sane went down very easily. I find it strange that the referee can give the penalty from where he is positioned," said Middlesbrough caretaker manager Steve Agnew.
Eight minutes later Boro went ahead again when Calum Chambers shot high into the net in a goalmouth melee after efforts from Stewart Downing and Negredo were kept out.
Brazilian teenager Gabriel Jesus, in his first start since returning from an injury layoff, had the last word with a fine header from Aguero's cross five minutes from time.
"To take the lead twice against a top team is something that is to the credit to my side. There are still nine points to play for and, with the spirit that the team has shown, there is no reason that we can't win more matches," added Agnew.
(Reporting by Rex Gowar, editing by Pritha Sarkar and Ken Ferris)
