Darren Bent put the visitors in front after just 15 minutes but Gary Cahill headed an equaliser on the stroke of half-time.
Marc Albrighton restored the advantage after 64 minutes and Ashley Young had a great chance to seal the points but saw his penalty saved by Jussi Jaaskelainen.
It proved costly as Cahill grabbed his second on 75 minutes and with four minutes on the clock Ivan Klasnic snatched victory for the home side.
