Neither side were at their best at the Etihad Stadium with clear-cut chances difficult to come by.
Pep Guardiola's men dominated possession and looked set to secure a late winner after Marouane Fellaini was sent off for headbutting Sergio Aguero, which sparked a frantic finale.
Substitute Gabriel Jesus had the ball in the net in injury time but the Brazilian's effort was chalked off for offside.
Aguero also missed an excellent opportunity at the death when he directed a shot wide of David de Gea's post from close range.
City stay fourth in the table on 65 points while United are fifth with a tally of 64.
But, crucially, the Gunners have 60 and will ramp up the pressure on their rivals if they win their game in hand.
Arsene Wenger's side, who have never failed to claim a place in Europe's elite competition during the Frenchman's tenure, also have two games in hand over Liverpool and will climb above Jurgen Klopp's men if they are victorious in both.
Arsenal are still likely to need to rely on other teams dropping points but Thursday's result represents a glimmer of hope for the north Londoners.