Substitute Bamford (76) curled home a fine effort from the edge of the box to keep the hosts in fourth place and maintain their promotion push.
Brighton had conceded only nine goals in 12 away games but they were beaten by a superb finish from the on-loan Chelsea striker whose second-half strike ended a run of three Derby defeats.
It was a moment of rare quality in a scrappy game of few chances although Derby 'keeper Lee Grant made a stunning save to deny Matthew Upson in the first half.
Derby skipper Richard Keogh returned to the team after missing five games with a knee injury but there were few alarms for either defence in a tepid opening until Jamie Ward cut in from the left flank in the 22nd minute and shot narrowly wide from 20 yards.
Brighton had enjoyed the majority of possession without really threatening but that changed in the 26th minute when Andrea Orlandi swung over a corner which Upson met with a bullet header only for Grant to produce a superb reaction save.
Derby's scoring record was being tested by a well-organised Brighton but the visitors composure was ruffled in the 38th minute when Simon Dawkins turned on the right-hand edge of the box and whipped in a low cross which was cleared at full stretch by Gordon Greer.
But those moments apart, the first half had lacked incident although Derby tried to raise the tempo after the interval only for a promising counter to break down on the edge of the visitors area.
Brighton created their best moment since the Upson header when they broke down the right in the 56th minute with David Lopez crossing deep for Orlandi to drive in a shot which struck Andre Wisdom before going behind.
Derby made a double change in the 59th minute with a tired-looking Will Hughes replaced by Jeff Hendrick while Bamford took over from Dawkins.
Brighton brought on Solly March for Orlandi in the 67th minute and Steve McClaren played his last card when he introduced striker Conor Sammon for Wisdom but it was an early substitution that changed the game.
Ward played a one-two with Bamford on the edge of the Brighton box in the 76th minute and when the ball broke back off a yellow shirt, Bamford showed class and composure in a tight situation to curl a left foot shot past Tomasz Kuszczak.
Brighton responded immediately with Leonardo Ulloa holding off a challenge to drive in a low shot which Grant did well to keep out but that was as close as they came to denying the home side.