They recovered from being two down at the break to earn a point, but the draw did not really help their play-off bid and they remain seven points adrift of sixth placed Brentford.
The home side started brightly enough and came close to ending the deadlock after 23 minutes. Chris Shuker produced a sublime chip over the Bradford defence for the on-loan Michael Chopra to gallop onto, but his lob over City keeper Paul Henderson came back off the far post.
To make matters worse it was Bradford who took the lead in the 27th minute. A dreadful error by Antony Kay let in Dean Windass and he coolly rounded Tykes keeper Ross Turnbull to slot in left footed.
Five minutes later Tom Williams brought down Nicky Summerbee and Windass did the business from the spot.
Barnsley boss Paul Hart clearly let rip at the break and the hosts were far better in the second half.
They pulled one back in the 54th minute with a wonderful 25-yard strike from Chopra - his 12th goal of the season.
The same player then twice tested Henderson in quick succession, while at the other end Windass was denied a hat-trick by Turnbull's brave block.
The chances kept coming for Barnsley and Shuker was denied by Henderson's legs from close range before the City keeper excelled with a great one-handed save from the unlucky Chopra.
Barnsley's efforts were finally rewarded two minutes from time when Stephen McPhail's free-kick was converted by Kay at the far post.