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The bonus point win for Gregor Townsend's men could prove vital in a tight Pool A that also involves Ireland and hosts Japan.
Victory was all but assured after a burst of 17 points in eight minutes late in the first half left Scotland 20-0 ahead at the interval.
Scotland wing Sean Maitland and Greig Laidlaw scored tries, both converted by the flyhalf who also kicked an early penalty, before fullback Stuart Hogg landed the Scots' first Test-match drop goal for more than five years with an audacious effort from just inside the halfway line.
Scotland secured the four-try bonus point with two penalty tries, Ed Fidow shown a pair of yellow cards that meant the Samoa wing saw red six minutes from time.
"We're all delighted to get that bonus point. It means we're still in this World Cup," said Scotland coach Townsend.
"We've two games to go and if we play like we did tonight and improve a couple of aspects, we're very much in this World Cup."
The Scots were in desperate need of a victory to have any hope of reaching the quarter-finals after starting this World Cup with a woeful 27-3 loss to Ireland -- who were in turn the victims of a shock 19-12 defeat by hosts Japan that threw Pool A wide open.
The Ireland reverse led Townsend to make wholesale changes, including fielding an entirely new back-row against Samoa.
The Pacific islanders were without centre Rey Lee-Lo and hooker Motu Matu'u after the pair received three-game bans for shoulder-led hits in a bruising 34-9 win over Russia.
It looked as if Laidlaw's ninth-minute penalty would be the lone score of a first half where both sides struggled to hold on to the ball in humid conditions under the closed roof of the Kobe Misaki Stadium.
In the error-strewn early exchanges, the biggest cheers went to a spectator playing the bagpipes, a traditional Scottish instrument.
But the character of the match changed on the half-hour mark when Scotland became the 20th -- and last -- team at this World Cup to score a try.
Flyhalf Finn Russell's superbly-judged cross-kick was caught by Maitland, who held off opposing wing Belgium Tuatagaloa for a try in the left corner.
Scotland had their second try just four minutes later.
Russell made a darting break before finding the recalled Jamie Ritchie.
The openside flanker's clever inside pass released Laidlaw, who fended off a poor challenge from Samoa fullback Tim Nanai-Williams before crossing by the posts for a try he converted.
Then, with nothing else on, Hogg dropped a goal from wide out on the left from just inside halfway, a distance of some 50 metres with the angle, to make it 20-0.
It was Scotland's first drop goal in an international since Duncan Weir's match-winner against Italy in March 2014.
Scotland, who have now won all four of their World Cup matches against Samoa, went further ahead before the hour.
Following a catch and drive off a close-range line-out, French referee Pascal Gauzere, after consulting the television match official, awarded a penalty try and sent Fidow to the sin-bin -- Samoa's third yellow card in two matches -- for collapsing the maul.
Samoa reserve scrumhalf Pele Cowley then came off the bench to play against his cousin Maitland for the first time in a Test but could not inspire his lacklustre side.
Instead Scotland had their second penalty try when Fidow went in knees first as Maitland tried to slide in at the left corner only to lose possession under the illegal challenge.
Gauzere showed Fidow a second yellow card and then a red.
Scotland next face outsiders Russia in Shizuoka on October 9, with Samoa playing Ireland in Fukuoka three days later.
Samoa coach Steve Jackson insisted his team were not out of the competition yet, with a tough game against Japan in only four days.
"If we get a result against Japan, we are right back in it. By no means do we think we are down and out," he told reporters.
Scorers:
Scotland 34 (20)
Tries: Sean Maitland, Greg Laidlaw, Penalty Try (2)
Conversions: Laidlaw
Penalties: Laidlaw
Samoa 0 (0)
Teams:
Scotland
15 Stuart Hogg, 14 Darcy Graham, 13 Chris Harris, 12 Sam Johnson, 11 Sean Maitland, 10 Finn Russell, 9 Greig Laidlaw, 8 Blade Thomson, 7 Jamie Ritchie, 6 Magnus Bradbury, 5 Jonny Gray, 4 Grant Gilchrist, 3 Willem Nel, 2 Stuart McInally (captain), 1 Allan Dell
Substitutes: 16 Fraser Brown, 17 Gordon Reid, 18 Zander Fagerson, 19 Scott Cummings, 20 Ryan Wilson, 21 George Horne, 22 Adam Hastings, 23 Duncan Taylor
Samoa
15 Tim Nanai Williams, 14 Belgium Tuatagaloa, 13 Alapati Leiua, 12 Henry Taefu, 11 Ed Fidow, 10 Tusi Pisi, 9 Melani Matavao, 8 Jack Lam (captain), 7 Thomas Ioane, 6 Chris Vui, 5 Kane Le’aupepe, 4 Teofilo Paulo, 3 Michael Alaalatoa, 2 Ray Niuia, 1 Logovii Mulipola
Substitutes: 16 Seilala Lam, 17 Paul Alo Emile, 18 Jordan Lay, 19 Piula Faasalele, 20 Josh Tyrell, 21 Pele Cowley, 22 Ulupano Seuteni, 23 Kieron Fonotia
