Samoa, whose previous best effort on the world stage was in 2000 when they also lost in the quarter-finals, had only an Antonio Winterstein try to show for their efforts in Saturday's quarter-final.
Fiji raced into an early lead after the impressive Akuila Uate broke through the Samoa defence and passed to Groom, who fended off two despairing tackles to score.
Naiqama converted the try and added two more points in the 10th minute with a penalty kick after David Fa'alogo's illegal shoulder charge.
Samoa suffered another blow after Penani Manumalealii went off with a suspected arm injury and was replaced by Mose Masoe.
The Samoans looked to create an opening after the 20-minute mark and Tim Lafai wrestled Uate into touch for a scrum in a promising position.
However, Anthony Milford's grubber-kick on only the second tackle was collected by Uate, who subsequently missed an opportunity to punish the full-back in the 26th minute.
As Fiji quickened the tempo, Kevin Naiqama threw a long pass to the explosive winger, but Uate dropped the ball in sight of the try-line.
The Fijians extended their lead in the 33rd minute with Naiqama's try, awarded by the video referee after a suspicion of offside.
An inventive grubber bamboozled Samoa winger Winterstein and allowed the opportunistic Naiqama to score easily and also add the conversion.
Samoa returned after halftime with renewed vigour, but they were forced to defend desperately when Marika Koroibete charged forward.
They finally struck in the 58th minute after their top try-scorer Winterstein dived in at the corner following an impressive period of quick ball.
Tensions boiled over in the 67th minute, as Lafai's crunching high tackle sparked a full-blown fracas, with referee Richard Silverwood quick to intervene.
Wes Naiqama's 100 per cent record with the boot continued when, from the resulting penalty, he pushed Fiji's lead out to 12 points.
Samoa tried to rally with fewer than 10 minutes remaining but couldn't find a way through Fiji's defence.
Fiji added gloss to the scoreline when Roqica went between the posts following some weak defending by their Pacific Island rivals.
The Fijiians' victory is also expected to earn them a place in the 2014 Four Nations Series in Australia.
- AAP
