Keller had to be alert to clutch a curling drive from David Jones after 23 minutes - and it proved vital as Fulham levelled seconds later.
Davies was the provider with the perfect cross from the right, and Kamara stole in to head powerfully past Roy Carroll.
Keller was in action again shortly after Kamara's goal, racing out to the feet of striker Kenny Miller as he closed in on Jones' pass.
It was the Scotland star's final meaningful contribution as limped off after 35 minutes to be replaced by Robert Earnshaw.
Fulham's set piece expert Bullard has wasted two opportunities from free-kicks, but he almost put his side ahead after 53 minutes with a left-foot shot that clipped the bar after he had been fouled by Hossam Ghaly.
There had been moments of entertainment amid the mediocrity, and Earnshaw almost took advantage of an ill-judged dash out of goal by Keller, but was just off target from an acute angle.
But Derby's luck was out with 12 minutes left when, after Carroll saved well from Kamara, Bouazza's shot took a wild deflection off Leacock and flew over the Derby keeper.
Derby's spirit was demonstrated, however, when they equalised two minutes later when Villa rose to head Mile Sterjovski's cross past Keller.
But there was to be no late reprieve and the Rams must now start planning for next season.
Fulham manager Roy Hodgson:
"We could have won it - and, of course, we're all disappointed at having scored a late goal which could have easily have been the winner only to let Derby straight back.
"Next week we must look for a much-needed win over Sunderland - and if we get that who knows? Every time we get a win people say we'll make it, and every time we lose people say we're doomed. I'm getting quite used to it.
"We won't be the last team to commit the cardinal sin of conceding a goal just after scoring. It's something we as coaches preach and warn players about - but it is an emotional game."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.