Torrential rain, which fell before the match and during the first half, threatened an abandonment as pools of water formed on the pitch.
But the rain stopped after the break and it was no coincidence that all three goals were scored in the second period.
Rantie, a £2.5million signing from Malmo, had only managed one previous goal for Eddie Howe's Bournemouth at Burnley in November and such were his celebrations at his 72nd minute goal that he earned a booking.
Lewis Grabban had given Bournemouth the lead from the penalty spot before Calum Woods equalised, ahead of Rantie's winner.
Huddersfield goalkeeper Alex Smithies was his team's hero in a sodden first half with a superb double save in the fifth minute from Elliot Ward and Harry Arter at the rebound.
Smithies also needed to dive to his right in the 15th minute to keep out a fierce shot from Matt Ritchie.
Huddersfield offered a threat on the break through Danny Ward and Tom Smith but it was Bournemouth who went ahead in the 55th minute.
Smith's clumsy challenge on Marc Pugh earned a yellow card and gave away the spot kick which was put away with ruthless efficiency by Grabban for his 12th goal of the season.
Huddersfield responded with an equaliser four minutes later with new signing Nahki Wells playing a key role in the build-up.
Wells sliced open the Bournemouth defence for Woods to race on and blast a left foot shot high into the net past goalkeeper Lee Camp.
Rantie came on for midfield player Andrew Surman in the 69th minute and got his landmark goal when Aston Villa target Eunan O'Kane set him up for a right-foot shot which went in off a post.
Huddersfield mounted late pressure in a bid to snatch a point and manager Mark Robins sent on veteran striker Jon Stead for the last few minutes and it almost paid off.
Stead laid on a comfortable chance for Ward in the dying seconds of stoppage time but the striker made a hash of his shot and Bournemouth escaped to claim a rare home win.