Bowyer put Blues in front with a header from point-blank range on 32 minutes but Junior Hoilett capitalised on a defensive blunder to grab Rovers a point seven minutes into first half stoppage time.
Hoilett pounced on an error by Liam Ridgewell to burst clear and beat keeper Ben Foster in a dramatic end to the opening period.
The second half was nowhere near as dramatic, with both teams ultimately forced to settle for a point.
Blues boss Alex McLeish named the same starting XI that had beaten Bolton last week after strikers Nikola Zigic and Obafemi Martins both failed late fitness tests.
Rovers carved out a fine chance in the opening seconds when Hoilett threaded a pass to Jermaine Jones in the box but the American slipped and his chance went begging.
Barely a minute had gone before home defender Martin Olsson became the first man in referee Chris Foy's notebook for a sliding challenge on Sebastian Larsson.
In a promising start by Rovers, captain Chris Samba came close in the fifth minute when he stooped to head a Pedersen free-kick just wide of Foster's right-hand post.
Ryan Nelsen headed a Pedersen corner into Foster's hands as the visitors struggled to get a grip on the game, offering little other than Cameron Jerome's scampering counter-attacks.
Blues grabbed the lead out of nowhere in the 32nd minute when Bowyer headed them in front after a cross by Jerome.
They came close to making it 2-0 two minutes before the break when Dunn fouled Craig Gardner and Larsson slammed the free-kick against the post.
A nasty-looking injury to Roger Johnson meant a lengthy period of stoppage time, in which Rovers grabbed the equaliser. Hoilett dispossessed Ridgewell and raced clear to round Foster and slot home.
Blues looked the better side early in the second half and Larsson once again came close from a free-kick which Robinson saved well.
Rovers came close in the 55th minute when Hoilett turned in the box and crossed for Santa Cruz, who headed against the top of the bar.
Rovers won a dangerous 75th-minute free-kick but Pedersen slammed a low shot into the Blues wall.
Rovers once again looked more likely to win it but clear-cut chances were few and far between in a scrappy final 10 minutes in which both sides' frustrations grew.