Huddersfield secured a League One play-off final place after a thrilling 4-2 win on penalties following a 3-3 extra-time stalemate.
Lee Peltier put the hosts in front in the 26th minute before Steve Lovell's penalty levelled, although Danny Ward put Huddersfield 2-1 up at half-time.
Lovell equalised in the 63rd minute for extra-time, and goals from Danny Ings and Antony Kay resulted in penalties.
But Bournemouth missed two penalties as Town booked their final place.
Liam Feeney and Anton Robinson missed from the spot as Huddersfield blasted all four of their kicks home, with Kay netting the winning spot-kick.
But Terriers captain Peter Clarke showed character by going over to shake several Cherries players by the hand before joining in his own team's celebrations.
Bournemouth have overcome much adversity in the past few years - battling administration, points deductions and transfer embargoes while losing highly rated players - and a manager - to higher division clubs.
A penalty shoot-out was a cruel way to end a run which has taken them from the brink of falling out of the Football League to within one game of the Championship - but it was a thrilling advert for the Football League.
Huddersfield had done their best to crank up the pre-match atmosphere by issuing their fans with folded cards, the rattling of which provided the soundtrack to the game - which was only 23 seconds old when Cherries keeper Shwan Jalal was called upon to make a reaction save from Roberts, who showed plenty of the trickery and skill on the ball that had worried Bournemouth in the first leg.
With Lee Clark's side playing at a high tempo, Roberts threatened again before Bournemouth had even got the ball out of their half, but Pearce had to put in a crucial block to deny the tricky Terriers winger.
The visitors first threatened with eight minutes on the clock as Lovell linked up well with his teenage strike partner Ings, who dragged his shot wide of Ian Bennett's post.
Roberts remained Huddersfield's creative spark, curling a shot wide, but the home fans' hearts were in their mouths when Adam Smith, on loan from Tottenham, was allowed to advance to within shooting range but drilled his shot just wide from 20 yards when eyeing up what would have been only his second senior goal.
Benik Afobe, who missed a gilt-edged chance in the first leg, burst down the right but Bournemouth managed to bundle his cross behind at the expense of a corner.
As at Dean Court, Roberts' delivery from set pieces was one of Huddersfield's most dangerous weapons, and although Jalal caught his first flag kick at the second attempt, he soon conceded another when he had to dive to his left to save well from Jordan Rhodes.
This time, Roberts managed to pick out Peltier, switched from right-back to central midfield for this second leg, to spark wild celebrations among the home faithful.
Bournemouth only threatened occasionally although Donal McDermott, scorer of their equaliser in the first game, forced a good low save from veteran keeper Bennett when the Terriers failed to clear their lines following a corner.
But when Smith burst forward from right-back once more, exchanged passes with Robinson and was brought down in the box, history repeated itself from Saturday as Bournemouth were awarded the chance to level the scores from 12 yards.
While Ings had been foiled by Bennett in the first leg, Lovell made no mistake, crashing his spot-kick into the roof of the net.
The Cherries had more trickery from Roberts to defend before the interval, but although Jordan Rhodes failed to direct his header on target when well placed, there was still time for Clark's men to retake the lead when Ward turned well to fire a fierce left-footed shot past Jalal in the dying seconds of the half.
Bournemouth soon had to withstand more pressure as Huddersfield pushed for a decisive third goal, while Roberts was at the heart of everything they created, but Rhodes scuffed a shot over the bar when it looked easier to score, while Ward drilled his shot straight at Jalal.
And they were made to rue those misses when McDermott raced down the left and fed Lovell, who dribbled round Bennett before finding the roof of the net for the second time - leaving the sides deadlocked once more.
Inevitably, Huddersfield looked to Roberts to fashion a third - but once more, Afobe's finishing was found wanting as he rode several challenges but ballooned his effort into the stand.
Clark was the more animated of the two managers by now as Bournemouth soaked up pressure from the home side while looking increasingly dangerous on the counter-attck.
Feeney's raid down the right earned the visitors a corner, from which he picked out Danny Hollands but his downward header was easily gathered by Bennett.
Roberts, whose man-of-the-match performance deserved a goal, cut in from the right but curled his shot wide of Jalal's far post - and the referee's whistle soon signalled the 30 extra minutes.
Extra time was barely 30 seconds old when a mix-up between Jalal and Shaun Cooper nearly let in Afobe, while the Cherries keeper did well to keep out Ward's shot from distance.
Roberts, orange boots glinting in the darkness, burst forward once more and was brought down by Hollands on the edge of the box, the midfielder earning a yellow card with the home fans baying for a straight red.
But when Michael Symes released fellow substitute Marc Pugh, the latter's left-wing cross was inch-perfect for the unmarked Ings to head past Bennett's despairing dive - and put the Cherries ahead for the first time in the tie.
However, with the visiting fans daring to dream of Old Trafford, Huddersfield hit straight back as another excellent Roberts corner was headed in by Kay to level the tie at 3-3 just before the end of the first period of extra time.
With penalties approaching, Jason Pearce was shown a straight red card for a foul, and boss Lee Bradbury immediately sacrificed Ings for French defender Mathieu Baudry as they battled to hold on.
And with Clark urging his troops forward for one last attack, Huddersfield were unable to make their one-man advantage - and considerable height advantage against a Pearce-less Cherries rearguard - pay.
But Huddersfield's unbeaten league run stretches to 27 games - and they can head to next weekend's Old Trafford final with that proud record intact.