Derby goalkeeper Lee Grant made a fine first-half save to deny Matthew Upson.
But although the visitors had the better of the few chances on offer, Bamford's class settled the game.
It was only the 10th goal the Seagulls had conceded in 13 away games and was a welcome relief to the home fans, whose side had lost three in a row in all competitions after an amazing run under manager Steve McClaren came to an end.
The Rams had the first chance of note after a dull opening 20 minutes when Jamie Ward cut in from the left wing and fired a 20-yard shot just wide.
Brighton's rare blank
Brighton's failure to find the net was only the second time in 15 matches they have failed to score.
But Brighton were having the bulk of possession and they finally threatened on 26 minutes when Upson's powerful header from Andrea Orlandi's corner forced a stunning reaction stop from Grant.
Derby, the Championship's top scorers, were struggling to breach the league's third best defence.
The pattern continued after the interval until the Rams made three changes, introducing Bamford, Jeff Hendrick and Conor Sammon.
Ward played a one-two with Bamford on the edge of the box with 14 minutes left and when the ball fell to the 20-year-old, he curled a left-foot shot past goalkeeper Tomasz Kuszczak.
Brighton responded with Leonardo Ulloa showing good strength to drive in a low shot that Grant did well to keep out, but that was as close as they came to an equaliser and defeat leaves them seventh, two points adrift of the play-offs.
Derby County manager Steve McClaren:
"Patrick showed great composure. There was no panic. We know he's got that quality and it needed a calm head in that situation.
"It's great when you have players who can change a game. It's not about 11 players - it's the squad, and we had 14 players who contributed to that win. In the modern game, it's absolutely vital because the game was going nowhere and we knew that at half-time.
"Jeff Hendrick came on, started in midfield and then went to right-back, which allowed Conor Sammon to come on so we could go to 4-2-4 and try and win the game, and Patrick produced that moment of quality to win it.
"It's a squad game. You need players who can come on and help change a game, and the squad won that game today, not the team."
Brighton boss Oscar Garcia said he did not select wantaway midfielder Liam Bridcutt because the player was not in the right state of mind to play:
"He said yesterday (Friday) he wasn't focused on the game 100 per cent. He was honest with us and, because of this, he didn't come with us.
"I had picked him to play today but he wasn't focused and in the next week, if nothing happens, I have to ask again. It's a problem between him and the club and they have to solve it as soon as possible.
"The best solution is as soon as possible because it would be better for the team, but these things happen in the transfer window.
"But I am not worried because the other players are fit enough and want to give 100 per cent for me and the club and I was proud of their performance today.
"We are looking to strengthen the squad and the club is working on a list of targets."
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