Boffelli scored an early try and converted four of five kicks from the tee to get Australian Michael Cheika's Pumas back to winning ways on Friday (Saturday AEST) after the disappointment of their 27-10 loss to 14-man England in their pool D opener.
England lead the pool with nine points from two games, four points ahead of Samoa, who beat Chile 43-10 in their opener, and third-placed Japan with Argentina in fourth place on four points.
Samoa managed just one penalty kick from former Wallabies five-eighth Christian Leali'ifano until replacement hooker Sama Malolo barged his way over the line for his third try of the tournament five minutes from time.
That set up a frenetic finale but Nicolas Sanchez, coming off the bench to win his 99th cap for Argentina, lashed over a final penalty from just inside the Samoa half to make the game safe.
After hot and humid conditions for the first two World Cup matches in Saint Etienne, autumn arrived with rain making for greasy conditions and a scrappy arm-wrestle of a contest between two physical teams.
Samoa made a calamitous start in the opening minute when fullback Duncan Paia'aua was shown a yellow card for taking out an Argentine in the air, presenting the Pumas with a chance to get some early points on the board.
Argentina struggled to convert territory into scores against England but had no problems in the ninth minute, cleverly stretching the undermanned Samoan defence to give Emiliano Boffelli space to cross the line out wide.
The fullback converted his own try and added a 45-metre penalty in the 24th minute with Leali'ifano, two days shy of his 36th birthday, finally getting Samoa on the board with a three-pointer of his own four minutes later.
Boffelli chipped over another penalty and the Argentina pack did well to hold out the Samoan eight from two five-metre scrums just before the break to go in at halftime with a 13-3 lead.
Argentina laid siege to the Samoan try line at the start of the second half and finally came away with some points when Boffelli kicked his third penalty in the 53rd minute.
Samoa had created little but almost produced a try of the highest quality on the hour mark when Alai D'Angelo Leuila poked a lovely grubber in behind the defence for Tumua Manu to chase.
But Boffelli beat him to it and the Pumas forwards got back to help him retain possession with Samoa threatening to steal the ball just under the posts.
