Bent headed in from close range in the first half but Chesterfield dominated possession for long periods and wasted good chances before Will Hughes sealed victory with a late solo effort.
Derby head coach Steve McClaren had switched to a 3-5-2 formation with Spanish centre-half Raul Albentosa making his debut while Bent made his first start alongside Chris Martin, but it was Chesterfield who almost scored in the second minute.
Eoin Doyle got behind Derby on the right and crossed to the back post where Armand Gnanduillet looked certain to score until Cyrus Christie made a crucial block, and then Doyle and Sam Clucas combined dangerously before Albentosa stepped in.
Derby were struggling to get any meaningful possession and although Hughes made a strong run into the visitors penalty area, Chesterfield had another good chance when Gnanduillet got in on the left only to shoot tamely at Kelle Roos.
But the home side took the lead in the 20th minute when Bent forced a corner and, after Jake Buxton headed the ball down, the former England man was first to react to head past Tommy Lee from two yards.
That was hard on Chesterfield but James O’Shea lifted the 5,000 plus away fans with a clever turn and shot from 25 yards that flashed just wide with Roos at full stretch.
Chesterfield were playing the better football and they created another chance in the 38th minute when a patient build-up saw Jimmy Ryan slip through on the right and he set up Clucas who fired over from 10 yards.
Although they were in front, Derby had looked far from convincing and McClaren replaced Albentosa with Johnny Russell at half-time, switching to a 4-3-3 and the Championship side should have scored again in the 51st minute,
Martin’s superbly-weighted pass sent Bent clear but Lee saved with his feet and when Russell broke through on the right six minutes later, Tendayi Darikwa slide in behind his goalkeeper to clear.
Derby were finding more and more openings and a mistake by Charlie Raglan in the 59th minute let in Bent but his lob was clawed away by Lee – and Chesterfield should have equalised two minutes later.
Daniel Jones crossed low from the left and the ball fell invitingly for Ryan 10 yards out, but the midfielder snatched at the chance and fired high over the bar.
The game had become really stretched and former Chesterfield favourite Jamie Ward, who replaced the injured Russell, ballooned a chance over before Simon Dawkins headed against Lee’s crossbar in the 71st minute.
Chesterfield kept pressing but Derby made the game safe in the 82nd minute when Hughes robbed Clucas outside the area and slipped past a defender before placing a right-foot shot past Lee.