Aston Villa are through to the Capital One Cup fourth round after bouncing back from a pair of Premier League defeats to beat local rivals Birmingham 1-0 on a tense night at Villa Park. Rudy Gestede nodded in the winner for the hosts but it was also a good night for boss Tim Sherwood, who made a pair of substitutions that transformed his team, following a lacklustre first-half display. Birmingham acquitted themselves with credit in front of a noisy derby crowd, confirming their improvements under boss Gary Rowett, but you sensed it may not be their night when Jacques Maghoma squandered a great chance to equalise. The match got off to a lively start and Gestede, who got the vote to start in attack for Villa, screwed a shot wide after neatly controlling an Ashley Westwood pass. Clayton Donaldson caused Villa plenty of problems for much of the night at the other end and, when he was tackled early on, the ball fell nicely for Maghoma, who advanced into the area before drilling a shot just wide of the post. However, Villa were the more vibrant side in the first 10 minutes and Scott Sinclair and Gestede were only crowded out by desperate defending in a goal-mouth scramble, before Blues keeper Tomasz Kuszczak bravely dived at the feet of Gabriel Agbonlahor to cut out a Leandro Bacuna cross. However, Birmingham really settled down after that and began knocking the ball around in assured fashion, albeit without posing a massive threat to the Villa goal. But the sight of a becalmed home side was enough to cause anxiety among the Villa fans and the hosts were booed at the break, after a Sinclair shot straight at Kuszczak was all they could muster in the closing stages of the half. Sherwood took remedial action and the introduction of Jack Grealish and Jordan Ayew for Joleon Lescott and Agbonlahor proved a masterstroke. Villa looked far more dangerous from the start of the second half onwards and a delightful Grealish cross caused panic in the Birmingham defence before the ball looped over the bar off Jonathan Spector. And the hosts then went in front when Grealish fed Jordan Amavi down the left and the full-back fired over a fantastic first-time cross which got the reward it deserved, Gestede (62) arriving on the penalty spot to power an unstoppable header into the net. However, Villa took their foot off the gas somewhat after scoring and were lucky not to be punished with 15 minutes left, Maghoma hitting a fairly tame shot straight at Guzan, having been put clean through on goal by a neat pass from Demarai Gray. Suitably chastened, Villa began to hunt for a second and created a string of chances in the closing stages. However, Kuszczak proved equal to a Sinclair free-kick and an Ayew shot, following an enterprising dribble, while the latter’s powerful cross-shot was too hot for Grealish to handle at the back post and Sinclair also side-footed wide. But one goal proved enough for the hosts, scenes of relief and jubilation greeting the final whistle after four minutes of stoppage-time. An emboldened Villa side will travel to Liverpool this weekend for their next Premier League encounter while Birmingham look set for a good season in the second tier on this evidence.