Barnsley had the better chances in a tight encounter.
Brian Howard went close before Diego Leon pulled his shot across goal on 34 minutes.
The ball dropped to Martin Devaney outside the area on 41 minutes but his shot hit the post and Jon Macken lost his footing and put the ball wide.
The second half was more open.
Barry Hayles should have scored from Lee Bell’s flick on but put the ball wide.
On the hour mark Leon’s corner from the right was met by the unmarked Stephen Foster but Paul Henderson palmed the ball wide.
Patrick Kisnorbo then blazed over for the visitors.
City made the breakthrough on 72 minutes as Hayles squared the ball to the on-rushing Hume, who tapped it past Luke Steele.