Sergio Aguero's early goal for City put Manuel Pellegrini's side in control, only for Osvaldo's brilliant effort to earn Southampton a point.
Both sides had chances to win the game in the second half, but title-chasing City had to be content with a draw against an energetic and resolute Southampton side missing a number of their key performers.
City broke the deadlock on ten minutes with the in-form Aguero netting his 18th goal of the season. Aleksandar Kolarov got down the left and sent over a cross for Aguero to rifle home with his left-foot 12 yards from goal.
Kolarov had a sight of goal himself four minutes later when he got on the end of a corner, but the defender flicked his effort just wide of the far post.
Southampton responded well to going behind and Jack Cork fired in a shot from 30 yards out which was well collected by Costel Pantilimon.
Aguero really should have doubled the lead on the half hour mark when Pablo Zabaleta got in behind the Southampton defence from Yaya Toure's fine pass and cut the ball back for his Argentine compatriot, but with the goal at his mercy he blazed his effort over the top.
Luke Shaw was looking dangerous for Southampton down the left and the full-back sent over a cross which James Ward-Prowse poked over the top under pressure from Kolarov.
Southampton should have drawn level on 38 minutes when Shaw sent over another brilliant cross from the left and fellow full-back Calum Chambers beat Kolarov to get on the end the delivery only to then head his effort wide of the target from inside the six-yard box.
Southampton continued to push City back in search of an equaliser and Ward-Prowse forced Pantilimon into a good save on 40 minutes with a swerving shot from the edge of the box which the City keeper did well to hold onto.
The home side drew level three minutes before the break with a superb solo effort from Osvaldo. The striker picked the ball up on the edge of the box and tricked his way past both Vincent Kompany and Zabelata before curling an inch-perfect shot into the top corner past a diving Pantilimon.
City wasted a great opportunity to restore their lead right on the stroke of half-time when James Milner's cross from the right found Samir Nasri inside the box, but the Frenchman blazed his effort wildly over the top.
The visitors created the first chance of the second half on 49 minutes when Zabaleta teed up Aguero inside the box and he hit a half-volley which was well palmed out by Paulo Gazzaniga.
A minute later Toure had a sight of goal and he was unlucky to see his powerful strike fizz just wide of the target with Gazzaniga well beaten.
Southampton should have grabbed the lead on 52 minutes when Pantilimon rushed from his line to take the ball off the feet of Jay Rodriguez and the ball dropped to Osvaldo who blazed over the top with the goal at his mercy.
Osvaldo had another chance two minutes later when Kompany's sloppy clearance fell into his path wide on the left-side of the box, but the striker dragged his left-footed effort of the target.
Southampton were on top now and Davis stung the palms of Pantilimon from 25 yards out before Osvaldo broke the City offside trap to get on the end of Adam Lallana's clever flick, but took long to get his shot away and City got players back to clear the danger.
The dangerous Aguero got clear of the Southampton defence on 67 minutes when he latched onto Toure's pass, but from a tight angle the striker dragged his effort wide of goal.
Southampton looked the most likely to grab a winner in the closing stages, but the City defence held firm.