The visitors created the best chance of the early stages through Greg Cunningham, who tested Wolves keeper Carl Ikeme with a right-footed drive in the fifth minute.
Kevin Doyle forced a save out of Tom Heaton at the other end, but the Robins should have taken the lead when Steve Davies found himself clean through on goal in the eighth minute, only to drag his shot wide.
City were gifted the lead in the 25th minute through a howler of an own goal by youngster Davis. The midfielder played a backpass to Ikeme that wrong-footed his goalkeeper and ended up in the net.
Things went from bad to worse for Wolves in the first period as manager Dean Saunders was forced to make two changes due to injuries.