Left-back Mirfin struck to earn the Terriers a deserved point 15 minutes from time and Peter Jackson's side would have gone on to win, but for two superb saves in the final ten minutes from Bournemouth keeper Neil Moss.
Bournemouth had the better of the opening 25 minutes but it was Huddersfield who had the first shot on goal when Danny Schofield sent a third minute volley just wide after Chris Brandon's corner had only been half cleared.
Striker Alan Connell had his goalbound shot deflected wide by defender Nathan Clarke 13 minutes later after being picked out by a Brian Stock corner.
Bournemouth did take the lead a minute later thanks to Spicer's first goal since completing a £10,000 move from Arsenal earlier in the month.
Warren Cummings caused chaos in the Huddersfield penalty area, beating two players before cutting in from the left and having the ball taken from his feet by goalkeeper Paul Rachubka.
Midfielder Spicer though was on hand to poke the ball home from the edge of the penalty area to make it 1-0.
Connell almost doubled the home side's lead with a speculative volley over the bar after he got in behind Clarke.
Huddersfield found themselves level in the 38th minute thanks to John McAliskey's sublime strike.
Defender Andy Holdsworth picked out McAliskey with a superb cross-field pass and the lanky striker calmly chested the ball down before volleying into the bottom left hand corner.
Spicer then volleyed Bournemouth back in front from a short corner six minutes into the second half.
Mirfin spared Huddersfield from defeat nine minutes later with the equalising goal.
Gareth O'Connor had already cleared off the line from McAliskey when Tony Carss picked out Mirfin from the corresponding corner and the defender headed past Moss.