The Pacific Islanders crossed five times as Duncan Paia'aua, Jonathan Taumateine and Fritz Lee scored and Sama Malolo grabbed two tries against the South Americans, who trailed by just two points at the interval.
Leali'ifano, 35, started for Seilala Mapusua's Samoa, four years on from featuring at the last edition of the World Cup for the Wallabies as the Pacific Islanders started their Pool D campaign.
Chile head coach Pablo Lemoine made four changes from last weekend's loss to Japan, which was Los Condores’ first game at a World Cup.
Leali'ifano opened the scoring with an early penalty before Chile responded as prop Matias Dittus found a way over from the bottom of a ruck on their first visit to Samoa's half before Santiago Videla converted to make it 7-3 after just seven minutes.
The try came to the delight of the pockets of Chilean fans in their team’s red shirts dotted among the 39 000-strong crowd in rugby’s heartland of the south west.
In the build-up to Dittus' touchdown Samoa centre UJ Seuteni was adjudged to have made a high tackle on Videla, and the midfielder was shown a yellow card.
Despite being down a man, Leali'ifano added two penalties and Samoa led 9-7 in glorious sunshine before Matias Garafulic made it a one-point game with a shot at goal of his own.
- Malolo double -
At halftime, Mapusua's side only led 17-10 due to Chile's impressive defensive line speed as Leali'ifano kicked a penalty and Seuteni made up for his earlier misdemeanour by assisting full-back Duncan Paia'aua, an uncapped former Australia squad member, for a try.
Samoa asserted their dominance after the interval and led 36-10 with 25 minutes to play as scrum-half Taumateine dived over from a delightful off-load by former basketball player Theo McFarland, flanker Lee scored from a maul and replacement hooker Malolo claimed the bonus point.
In the final quarter, both sides spent time with inferior numbers on the pitch as Chile flanker Alfonso Escobar and prop Esteban Inostroza as well as Samoa scrum-half Ereatara Enari were shown yellow cards.
Escobar's high tackle on Lee became the latest example of inconsistent refereeing decisions during the World Cup surrounding head-high challenges.
Samoa rubbed salt into the wounds with the clock in the red as Malolo claimed his second try of proceedings as Mapusua's team, outsiders to reach the knockout stages, began their campaign on a positive note.
