The visitors were far the better side in the first half but wasted several chances after Matt Ritchie hit a post and Derby made them pay when Martin grabbed his 18th goal of the season five minutes from time.
He curled a 20-yard free-kick into the top corner to clinch another three Sky Bet Championship points for Derby, who remain two points behind second-placed Burnley - who they play next Saturday.
Jamie Ward, who scored Derby's winner at Bournemouth in November, was out with a hamstring injury and key midfielder Craig Bryson also missed out with a thigh problem which meant starts for Jeff Hendrick and Johnny Russell.
Bournemouth's Eunan O'Kane was replaced in midfield by Andrew Surman as the visitors tried to halt a side that had won four of their last six games.
Matt Ritchie was close to giving the visitors a shock lead in the 16th minute. A Derby raid down the right was halted by a superb tackle by Simon Francis on Russell and Bournemouth broke swiftly, with Ritchie smashing a low shot from 18 yards against the foot of Lee Grant's left post.
There was another scare for Derby in the 20th minute when Tokelo Rantie set up Lewis Grabban, who drifted across the box before firing just wide and Rantie's pace almost forced Richard Keogh into putting the ball into his own net three minutes later.
Bournemouth had another chance in the 27th minute when Grabben cleverly turned Andre Wisdom and raced clear on the right - but his finish lacked the power to beat Grant, who saved easily.
Derby had been flat and they made two changes at the start of the second half with Connor Sammon replacing Patrick Bamford and John Eustace giving way to Simon Dawkins.
There was certainly more urgency about the home side and the two substitutes combined in the 53rd minute when Dawkins pulled the ball back from the left and Sammon was foiled at the near post by ex-Derby goalkeeper Lee Camp.
Derby were starting to pressurise the Bournemouth defence and they almost scored in the 67th minute when Martin's low cross found Russell at the back post but he was denied by a goal-line clearance.
The goal Derby had been threatening finally arrived in the 85th minute when Will Hughes was tripped just outside the box and Martin curled his free-kick from 20 yards over the wall and into the top left corner of Camp's goal.
It was tough on Bournemouth, although they had created little in the second half and they could not find a reply as the hosts celebrated a hard-fought victory.