Ten-man City suffered a self-inflicted defeat at Bristol Rovers - but left frustrated that they were not given a late chance to grab a point from the penalty spot.
The Bantams were trailing to two poor goals and then had Rob Kozluk sent off, their fifth player to see red this season.
But David Syers pulled one back on his comeback from a three-game ban to set up a stirring finish.
And the depleted visitors thought they had clinched a comeback when sub Kyel Reid appeared to be tripped by Chris Zebroski. But nothing was given and City were left empty-handed.
New Rovers boss McGhee was handed a dream start in his first home game when his side struck after six minutes from the opening corner.
City had three chances to clear but the ball eventually skimmed off Lee Bullock and fell to Lee Brown who had loads of space to fire into the bottom corner.
There were half-hearted appeals for offside but it was a sloppy goal that should have been avoided.
New boy Will Atkinson showed great control to bring down a long clearance and set up Craig Fagan. But the skipper's first-time drive flew wide.
Fagan hooked another chance over and Marcel Seip blazed off target while Chris Zebroski shot tamely at Jon McLaughlin for the home side.
Nahki Wells was City's busiest player and delivered a dangerous cross which Michael Poke just managed to flick away from the incoming James Hanson.
Rovers thought they should have had a penalty just before the break after Eliot Richards went down from Fagan's challenge. It looked a strong claim and there was relief in the City ranks when Chris Sarginson waved the appeals away.
McLaughlin looked uncomfortable dealing with Andy Dorman's cross-shot and Matt Gill fired wide as the home side finished the half strongly.
City's hopes of hitting back in the second half suffered another blow ten minutes in after an uncharacteristic error from Andrew Davies.
The centre half got caught in possession midway inside the City half and Richards nicked the ball away before beating McLaughlin.
And City's problems grew when Kozluk was shown his second yellow card after 65 minutes after catching Richards late.
But the ten men, now playing three at the back, climbed off the canvas seven minutes later. Sub Deane Smalley headed into the mix and Davies and Syers threw themselves at the loose ball, the midfielder getting the decisive touch home.
McLaughlin kept the hopes alive by denying Richards, who then hit the post through a crowd of players from the resulting corner.
City were giving it a go to rescue a point and almost had it with a Davies header which Poke clawed round the post.
McLaughlin spread himself well to thwart Richards once more as City piled forward.
And like Rovers in the first half, they were fuming at Sarginson for turning down a late claim for a spot-kick after Chris Zebroski's challenge on Reid. It looked nailed on but the referee remained unmoved.
Phil Parkinson and the coaching staff spilled on to the edge of the pitch in their frustration and the Bantams boss raced over to confront the referee at the final whistle.
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