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The stoppage-time equaliser ended Burnley's faint chances of automatic promotion and means they will have to go through the play-offs to reach the Premier League.
There seemed to be no sign of a way back for the home side who had played with spirit and commitment in the first half but created few chances in the second.
They had handed Burnley a 59th minute goal which Chris McCann gratefully accepted and the visitors were seconds away from what would have been a fifth victory in six Championship games when they lost concentration.
But Derby deserved something from what was a competitive and at times rugged contest and could justifiably claim they should have had a penalty when Kris Commons was barged over from behind by Graham Alexander in the 36th minute.
It was one of the few errors Alexander made before the midfielder was taken off nine minutes from the end which ended his record of having played in every minute of Burnley's 53 matches this season.
But even without their influential enforcer, Burnley appeared to be coasting to three points courtesy of the soft goal Derby conceded early in the second half.
Although Chris Eagles delivered an excellent cross from the right, Stephen Bywater was about to grab the ball until he ran into Martin Albrechtsen leaving McCann to tap the ball over the line.
Derby had tested Brian Jensen on four occasions in the first half but they hardly threatened his goal in the second period until the final minute of stoppage time.
Burnley allowed Gary Teale to get the ball out on the left and he delivered an excellent cross that Connolly met with a diving header to cut short the celebrations of the visiting fans.