Antony Kay struck the winning penalty after a thrilling night at the Galpharm Stadium to send the triumphant Terriers to Old Trafford on May 29.
The Terriers defender held his nerve to smash home high into the roof of the net to extend his side's unbeaten run to 27 matches and set up a showdown with MK Dons or Peterborough, who play on Thursday.
Bournemouth, whose skipper Jason Pearce was shown a straight red card in extra-time, missed two of their four penalties in the shoot-out.
Huddersfield goalkeeper Ian Bennett saved Liam Feeney's effort and then Cherries midfielder Anton Robinson hit the crossbar, while Lee Novak, Danny Ward, Kevin Kilbane and Kay all scored.
Defender Lee Peltier's opener was cancelled out by Bournemouth striker Steve Lovell's penalty, but Danny Ward's fine individual effort sent the home side in 2-1 ahead at half-time.
Journeyman striker Lovell then fired his second of the night to haul Bournemouth level again just after the hour.
Cherries striker Danny Ings headed his side in front 14 minutes into extra-time, but Town defender Antony Kay crashed home another header in the 105th minute to ensure the tie went to penalties.
Peltier won his fitness race after limping out of the first leg with a hamstring strain, but was deployed in central midfield, with Jack Hunt continuing at right-back.
Bournemouth were unchanged from the side that started the first leg on Saturday, which ended in a 1-1 draw.
The hosts almost scored inside 25 seconds when winger Gary Roberts' shot, following Benik Afobe's knock-down, was brilliantly parried by Bournemouth goalkeeper Shwan Jalal.
The tempo was unrelenting and Huddersfield made the breakthrough in the 26th minute.
Roberts swung over a corner - after Jalal had saved superbly again to turn away Jordan Rhodes' header - and Peltier nodded home unchallenged at the far post.
But after spending most of the first half on the back foot, Bournemouth were awarded a penalty a minute before the break.
Home skipper Peter Clarke tripped visiting defender Adam Smith and Lovell thumped his spot-kick high into the roof of the net.
With barely 60 seconds to contemplate any injustice, a moment of individual magic then lifted Huddersfield back in front.
Ward, with his back to goal on the edge of the penalty area, turned in a flash to wrong-foot his marker and fired a left-footed shot beyond Jalal into the bottom corner.
Huddersfield burst out of the blocks at the start of the second period and from one of several corners Clarke's sidefooted effort was deflected inches wide.
But Bournemouth were not for rolling over and in the 63rd minute, when Donal McDermott's cutback from the left caught the home defence off balance, Lovell pounced, riding one tackle and then waltzing around Bennett before slamming home his second goal of the night.
Huddersfield winger Roberts curled an angled shot from 20 yards wide in the 88th minute, but with players on both sides already wilting, the game went into extra-time.
Ward rifled a low shot straight at Jalal and Kay swung a tired leg to lift the ball high and wide as the home side pressed.
But still Bournemouth refused to bow and when Michael Symes sent fellow Cherries substitute Marc Pugh racing clear down the left, the latter's pinpoint cross was headed expertly home by Ings.
The Terriers had to respond - and right at the end of the first period of extra-time they did.
Roberts swung over a corner and Kay hauled himself above the Bournemouth defence to crash home his header to level the match for a third time.
Bournemouth captain Pearce was shown a straight red card for his two-footed lunge on Kilbane in the 112th minute, but the Cherries held on and the tie was decided on penalties.