Pisi contributed 15 points thanks to the accuracy of his boot, with a scrappy affair between the Pacific island nations eventually coming to life in the final 20 minutes with three tries.
Kahn Fotuali'i and George Stowers crossed for the Samoans, with Fiji's reply coming from Netani Talei .
Both teams had beaten group whipping boys Namibia earlier in the tournament but had suffered one defeat each as well, with Samoa losing to Wales and Fiji outplayed by South Africa.
It was Samoa who got the first points on the board with Pisi's sixth-minute penalty after their opponents were punished for not rolling away in the tackle.
Samoa were then denied the opening try moments later when centre George Pisi's slide for the line, a result of Paul Williams' break, was impressively held up by winger Naipolioni Nalaga.
However, fly-half Pisi was successful with another penalty attempt soon after and then landed a lovely drop goal to stretch Samoa's lead to 9-0 after 13 minutes.
The contest was becoming increasingly untidy and another unforced error allowed Pisi to add three more points to Samoa's tally, while Fiji were awarded their first penalty on the half-hour mark but Seremaia Bai pushed it wide.
That left Samoa with a 12-0 advantage at the interval and Pisi extended that four minutes into the second half with his fourth successful penalty kick.
Fiji were at least showing signs of improvement and launched an attack soon after, only to be held back close to the line by some dogged defending.
Samoa were eventually the first to cross the line after 62 minutes. The ball was played out wide to the left with Pisi making a dash for the line. The fly-half was stopped but Fotuali'i continued the move and his determination saw him over.
Pisi was unable to add the extras, but the score was the catalyst the match needed.
Fiji responded after 67 minutes with their first points, a converted try for blindside flanker Talei after some patient build-up play.
Two minutes later, Fiji's defence was breached again by Williams, who found a gap and raced through before laying the ball off for Stowers to dive over in the corner.
Williams converted to restore Samoa's 20-point advantage, with a late attempt from Fiji to cross again and restore a little more pride coming up just short.
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