Manchester City made it six games without a Premier League win at Eastlands after being held to a 0-0 draw by Wigan on Saturday evening.
The visitors should have taken the lead in the 15th minute when Antonio Valencia beat two men and pulled back for Wilson Palacios, who completely missed his kick from 12 yards out.
And Benjani should similarly have put City ahead just after the half-hour mark. The striker was put clean through by Stephen Ireland but he failed to get the ball properly under control and Chris Kirkland was able to rush out and block before Erik Edman cleared the loose ball.
Benjani went onto miss the best chance of the game in the 70th minute when he volleyed wide from six yards, while Palacios forced Joe Hart into a good save nine minutes from time as Latics went close to an unlikely winner.