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Bradford then almost scored in the 20th minute as a stray ball ricocheted off Matthew Pennington and into the side-netting.
A warning sign was to come as Tudgay headed wide from Aaron Phillips's cross two minutes before the break, and just moments later, Nouble latched on to another Phillips ball to poke home from close range.
It was a sign of things to come because, in the 68th minute, Martin's challenge on Andy Halliday led to a Bradford free kick outside the box, which Yeates lashed past Burge and into the far corner.
Coventry set about trying to regain the lead in the latter stages, but despite dangerous efforts from Noble and Nick Proschwitz, they were unable to score again.
Bradford very nearly had the final say when Hanson sent a header towards goal from close range in the 90th minute, but Burge was able to dive to his right and pull off a smart save.
The result keeps Coventry just above the drop zone in 20th place, while Bradford stay ninth.