Mark Hughes kept a largely unchanged side from the one that faced Hamburg in midweek, resting only Micah Richards to bring in Nigel De Jong, who was cup-tied in midweek with Pablo Zabaleta returning to right-back.
West Brom were aggressive from the start, carving out plenty of chances to score by an sleepy City defence, including a flurry of early chances in which the luckless Abdoulaye Meite contrived to miss from five yards out with only Shay Given to beat.
The Baggies' defensive record hasn't been the greatest this season though and Robinho notched up his first City goal of 2009 with a sweetly struck volley from Stephen Ireland's cross in the eighth minute.
Nedum Onuoha made it 2-0 after just 20 minutes when he pounced on a poor headed clearance by Meite to nod home. Scott Carson, the West Brom keeper, was booked for vociferously protesting about the goal to the referee.
It might have looked comfortable for the home side, but it wasn't long before Albion finally began to convert some of the chances that came their way.
City were thankful for Felipe Caicedo's goal-line intervention to deny Robert Koren's effort following Given's shaky clearance after 32 minutes, before Tony Mowbray's men started to get some reward for their hard work.
Chris Brunt's 38th minute daisy cutter beat Given after Marc-Antoine Fortune's lay-off found the Baggies winger in acres of space.
Brunt levelled the scores after half-time after Fortune was brought down 25 yards out from goal. His sweetly struck 54th minute free-kick curled past everyone in the area to beat Given, who saw it late and got nowhere near it.
The pressure was on, but City immediately replied after Elano earned a penalty right from the restart. Jonas Olsson hauled the Brazilian down in the area and Elano stepped up to send Carson the wrong way.
With City finally feeling the after-effects of the Hamburg match late on, West Brom attacked continually in the closing stages of the match and City found themselves hanging on with just ten men after Zabaleta hobbled off shortly before full-time with all substitutes used up.
However, super-sub Daniel Sturridge popped up to finish off the visitors deep into injury time.