Tonga broke the deadlock after nine minutes as Glen Fisi'iahi picked out a gap in Scotland's defense to find the try line, but efforts from Matty Russell, Ben Fisher and Brett Carter, plus a Danny Brough penalty gave Scotland a comfortable 20-4 lead at the break.
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After having two tries ruled out by the video referee, Manu managed to add a second to leave his side just two points behind the Scots, before Willie Manu collected the ball following a lengthy run from Daniel Topou to put Tonga back in front.
Russell managed to force his way through the Tongan defence eight minutes from full time to add Scotland's only points of the second half and put them back ahead.
Daniel Foster thought that he had added a sixth try of the match for Tonga late on, but it was not awarded after replays showed that the ball had not been grounded.