Hobbs, signed on loan from Hull over the summer, headed home four minutes before half-time to preserve Forest's unbeaten record at the City Ground and inflict a first away defeat of the season in the Sky Bet Championship on the Rams.
The margin of victory could have been greater than 1-0 had Darius Henderson not fluffed a second-half header and a late penalty.
Derby, who had captain Richard Keogh sent off for the challenge on Chris Cohen that resulted in the spot kick, created very little in way of scoring opportunities.
The pre-match build up had all the sub-plots of a soap opera.
Billy Davies and Nigel Clough renewed acquaintances, each manager inextricably linked with the opposing side.
Davies took Derby up to the Premier League in 2007, while Clough began his career as a trainee with Forest, whom he supported as a boy and arguably enjoyed his best years as a player under his father Brian who is synonymous with the history of the two clubs separated by 17 miles of the road which bears his name - Sir Brian Clough Way.
The latest chapter in the fixture's rich tapestry saw Forest begin with a good tempo and start the match on the front foot.
A good first touch from Radoslaw Majewski allowed the Pole to get a left-foot shot away from just outside the area after eight minutes which Lee Grant diverted wide with his fingertips.
Despite the early dominance of Davies' team, that was all Derby really had to worry about and by the midway point of the first half the Rams had settled into the game.
A swerving long-range effort from Craig Bryson then had Karl Darlow scrambling across his goal but the ball swung wide of the post.
Johnny Russell should have put the visitors in front in the 39th minute. The Scot beat his marker to Craig Forsyth's cross but mistimed his header from six yards out and the ball flicked off the Forest defender and harmlessly into the path of Darlow.
It proved costly as two minutes later the Reds edged ahead.
Eric Lichaj's shot deflected narrowly over the crossbar off Jake Buxton's head and from the resulting corner, Hobbs arrived unmarked at the near post to power a header past Grant.
The Derby goalkeeper made an important block at point-blank range to thwart Jamie Mackie in first-half injury time and Forest spurned another opportunity for a two-goal cushion on the hour mark when Henderson made a mess of his header six yards out.
A rare second-half chance for Rams came when home substitute Djamel Abdoun brought down Adam Smith right on the edge of the area. Will Hughes took the free-kick but his curling effort lacked conviction and Darlow, diving to his left, plucked the ball out of the air.
Forest had a glorious chance to double their lead with 12 minutes remaining.
A surging midfield run from Cohen was halted by Keogh's challenge from behind. Referee Simon Hooper pointed to the penalty spot and showed the Rams skipper a second yellow card - but Henderson's spot-kick was brilliantly tipped round the post by Grant diving down to his right.
Conor Sammon had a late chance to rescue a draw for Derby but that would have been harsh on Forest, who themselves were denied a second goal when Grant denied Andy Reid in injury time.