However a second try for Harries with late efforts by replacement scrum half Laura Prosser and skipper Jamie Kift made the game safe for Wales.
Rhian Bowden had an outstanding game for Wales, constantly crossing the gain line with a series of bullocking runs but it was a piece of individual brilliance by the hooker which brought the crowd to their feet on the stroke of halftime.
Having demanded the ball from fly half Awen Thomas, Bowden tore into the Swedish defence. Despite having defenders crawling all over her, she off loaded a magical flip ball to Mel Berry which Paul Daniels would have been proud of and the Welsh No8 scorched over from 35m to give Wales a comfortable lead at the break.
Wales's lead could have been even more impressive but twice Catrin Edwards was denied five pointers by the referee when the powerhouse prop had appeared to score.
In the second half Wales lost their shape as Sweden attempted to get a foothold into the game. Eventually Westin-Vines crossed the whitewash to bring Sweden within two scores of Wales.
But despite having plenty of possession Wales were unable to make their superiority count until a double salvo by Prosser and Kift in the dying stages ensured Jason Lewis's team take on South Africa on Sunday for ninth position.
Scorers: Wales: Tries - James, Harries (2), Berry, Prosser, Kift; Con - Thomas.
Sweden: Try: Westin-Vines; Con - Norman; Pen - Norman