The British number two had been hoping to build on a semi-final appearance in Atlanta, but he went down 7-5 4-6 6-3 to the fourth seed.
During the opening set, as many as 10 break-point chances were created by both players but it was the sole conversion from Dimitrov which saw him move closer to the next round.
The world number 11 created four more chances in the second but Edmund saved each of them, while taking his own opportunity to force the match into a decider.
Edmund won more receiving points during the final set but Dimitrov claimed the only break of serve to run out the victor in two hours and 21 minutes.
Twenty-two-year-old Edmund will now head to the Masters Series event in Montreal as he continues his preparations for the US Open.