Veteran Terriers midfielder Kevin Kilbane, 34, opened the scoring at Dean Court in the 22nd minute on Saturday with a fine header from Gary Roberts' right-wing cross.
Thirteen minutes later, Terriers goalkeeper Ian Bennett made a fine save to deny Danny Ings from the penalty spot but the Cherries rallied in the second half and were rewarded when midfielder McDermott fired home a fine left-footed strike from 25 yards.
The return leg takes place at the Galpharm Stadium on Wednesday and Lee Clark's men, who extended their remarkable unbeaten run to 26 games, will be quietly confident of booking their place in the play-off final at Old Trafford later this month.
They did not hit top gear and it was Bournemouth, whose form has fluctuated since Eddie Howe jumped ship to join Burnley and Lee Bradbury was placed in charge, fashioned the first opening in the ninth minute.
Defender Jason Pearce headed the ball over the crossbar from 12 yards and the Cherries went close again in the 16th minute when McDermott hit a shot from 18 yards which Antony Kay blocked.
Huddersfield gradually steadied themselves and opened the scoring in the 22nd minute when Kilbane powered home Roberts' cross with a fine header.
The Terriers sought to extend their advantage in the 25th minute when midfielder Scott Arfield was afforded the time and space to advance forward and struck a shot from 20 yards.
However, Bournemouth could have been level in the 35th minute after Bennett brought down Rhoys Wiggins inside the penalty area.
Ings stepped up to the spot from 12 yards but Bennett made a fine parried save to thwart his right-footed effort.
Danny Ward, on loan at Huddersfield from Bolton, then hit a shot from 25 yards which Pearce did well to block.
The Terriers went close again in the 39th minute when Roberts hit a blistering drive from 25 yards which Bournemouth goalkeeper Shwan Jalal tipped over with a superb save.
Two minutes before the break, Roberts flighted an inswinging corner which Kay greeted with a firm header that flew just wide.
Yet Bournemouth began to enjoy more possession in the second half and were rewarded on the hour when the ball was worked to McDermott, who drove a low, left-footed shot into the net from 25 yards.
Bournemouth could have led three minutes later when Danny Hollands crossed and Anton Robinson headed wide from 12 yards.
Joey Gudjonsson twice threatened from distance for Huddersfield but the Cherries held firm to leave the tie finely poised ahead of the decisive second leg.