Davenport's twelfth minute header was followed by Grzegorz Rasiak's overhead kick to give the visitors a two goal lead at half time.
Lee Barnard, twice, and Simon Dawkins also beat Joe Lewis, although City can count themselves unlucky not to have had a penalty, while Davenport had to clear off the line from Rossi Jarvis.
Andy Hughes completed the first half on his way back to full fitness, and should now come into contention for a place in the team to face Watford at the weekend.