
The hosts took the lead within eight minutes after Phil Neumann volleyed home following a free kick from Demarai Gray, before Jhon Solis added a second for Birmingham after a mix-up at the back in the 29th minute.
Tomi Horvat's penalty kick cut into Blues’ lead in the closing stages, and while the Robins had late opportunities in injury time, they were unable to mount a comeback, and the hosts held on to secure all three points.
The defeat sees City fall to 13th in the Championship table going into the final game of the campaign, when they will return to Ashton Gate to take on Stoke City.
Interim head coach Hodgson chose to stand by the same team that shared the points at Southampton in midweek, with Delano Burgzorg and Sam Bell preferred to Mark Sykes and Emil Riis. On the bench, Adam Randell was cleared to return after missing the previous fixture on the south coast with a dead leg.
The first opportunity of note fell to Scott Twine, as he unleashed a shot from the edge of the penalty area, which was tipped over the bar by Blues goalkeeper James Beadle.
But just moments later, the hosts found the opener, as Neumann was left unmarked in the box to volley Demarai Gray’s deep free kick past Radek Vitek and into the back of the net.
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At the other end, Beadle was called into action with an acrobatic save to turn a curling Tomi Horvat cross away for a corner, after the ball looked as though it may sneak in at the far post.
Gray next came closest for the hosts, as his direct free kick whistled narrowly wide of the left stick, before he followed up with another opportunity soon later, though his right-footed effort was well dealt with by Vitek.
An error at the back allowed Birmingham to extend their lead in the 28th minute, as Sam Morsy inadvertently skewed his pass into the path of Solis, who was left open to shoot from the centre of the box. A scrambling Radek Vitek attempted to get back across his goal to claw his effort away, and while he did get a hand to it, the ball had already crossed the line, leaving City trailing by two at the break.
The hosts continued their strong start in the second half, with August Priske finding himself one-on-one with Vitek within six minutes of the restart. The Dane lifted his shot over the Manchester United loanee, and it looked as though he would find the bottom left corner of the City net, but he was denied by the post.
The striker followed up his effort just moments later with a left-footed shot from the centre of the box, but he was unable to direct it on target before a powerful long-range attempt from Jay Stansfield forced Vitek into another crucial stop.
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Hodgson opted to make a double change in the 63rd minute, which nearly saw an immediate reward, as Horvat attempted to play a pass in towards Emil Riis, though the City substitute was unable to get a touch to poke home from close range.
With just eight minutes remaining, the Robins were awarded a penalty after Stansfield was judged to have fouled Horvat on the right side of the area. The Slovenian international made no mistake from the spot, as he aimed to the left and sent Beadle the wrong way.
The Reds came close to claiming a point in added time, as Horvat delivered a free kick into the box, which was met by Ross McCrorie, who headed towards the far post, but Riis was unable to get the crucial touch to bundle the ball over the line.
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