Graham Dorrans had given the Baggies a first-half lead at Ashton Gate but home side Bristol City staged an excellent comeback after the break and took all three points thanks to Chris Iwelumo and Lee Johnson.
West Brom remain one point behind Nottingham Forest and now have just one game in hand on the Reds.
They face Derby County at home next Saturday while Billy Davies takes his team to the Walkers Stadium to face Leicester City.