Two late goals from Chris Burke and a first half header from Paul Robinson ultimately saw Blues cruise through to the fourth round of the FA Cup with Budweiser.
Lee Clark made just three changes to his starting XI. Colin Doyle, Shane Ferguson and Reece Brown were introduced in place of Darren Randolph, Wade Elliott and Callum Reilly respectively. For 17-year-old Brown it was the first time he had started a game for Blues.
Rovers came close to taking a third minute lead when Eliot Richards found himself through on the Blues goal and with just Colin Doyle to beat, but fortunately the Blues keeper saved his shot with his legs.
With the rain pelting down on the pitch, Robinson tried his luck with a 35-yard pile-driver that sailed just wide of the post.
Minutes later Blues should have broken the deadlock when Paul Caddis’s cross found Nikola Zigic, but the Serb headed wide from close-range.
Blues started to pile on the pressure and in the space of a few seconds Caddis had two goal-bound shots blocked, before Lee Novak saw his effort cleared off the line.
The slippery conditions were making it difficult for either team to get a real foothold in the game. That was until Blues took the lead after 35 minutes through captain Robinson who netted his first goal for the club. Ferguson sent in a deep corner to the far post where the centre-half was waiting to head the ball home from just six yards out.
As the game entered stoppage time at the end of the first half Mitch Hancox went on a mazy run deep into the Rovers half before trying his luck from distance with a low shot, which Rovers keeper Steve Mildenhall held onto at the second attempt.
Less than two minutes after the restart Blues had a great chance to double their advantage when Caddis’s cross found Zigic just six-yards out, but the striker headed his effort straight at the keeper.
Blues continued to hunt for a decisive second goal and were posing much the greater attacking threat.
Just after the hour mark Olly Lee tested Mildenhall with a stinging strike from distance.
But Rovers were certainly not out of the contest and Doyle was forced to produce an excellent save to push Lee Brown’s goal-bound free-kick over the bar.
Backed by a vociferous travelling support of almost 2,400 fans, Rovers carried on looking for an equaliser in the dying minutes but it was Blues who put the game beyond doubt with two quick-fire goals from Burke.
Zigic was the provider for his first on 85 minutes after he slid a great ball through to the Scot who side-footed it home. The second came after Caddis laid the ball back to him and he found the bottom corner from 18 yards out.
Blues will now play top flight Swansea City in the fourth round of England’s premier cup competition over the weekend of January 24/25 .