Southampton took the lead when Redmond pounced on a back pass from John Stones intended for Vincent Kompany, the City captain making his first PL appearance since 19 April, and rounded Claudio Bravo to silence the Etihad Stadium.
Stones thought that he had made amends shortly afterwards when he connected with Kevin De Bruyne's free-kick, only to be denied by an offside decision against Sergio Aguero.
Iheanacho replaced De Bruyne at half-time and within 10 minutes had equalised, meeting Leroy Sane's low, left-wing centre.
City threatened a second with Ilkay Gundogan and Iheanacho thwarted by Fraser Forster but City, who move on to 20 points along with Arsenal and Liverpool, had to settle for a point.
The Premier League website employs cookies to make our website work and improve your user experience. Essential cookies are required for the operation of our website. You may disable these but this may affect website functionality. Non-essential cookies help us improve the functionality of our website by collecting information and reporting on your use of the website as well as improving your user experience. You can manage your cookie settings and switch off non-essential cookies via the “Manage Settings” below.