Last year's runners-up Switzerland led 8-7 going into the 10th and final end, but having already scored three in the eighth to turn the tie on its head, two more points from skip Eve Muirhead at the death secured a vital win.
Meanwhile, 2018 bronze medallists Germany got their first win of the competition - overcoming Czech Republic 9-8 - and defending champions Sweden beat Latvia 9-2.
There were also wins for Russia and Norway – 9-3 over Denmark and 7-6 over Estonia, respectively.
Muirhead snatches Scotland win with final stone
Hosts Sweden maintained their unbeaten start in the men's competition, with a 9-4 victory over England in the morning session of day three in Helsingborg.
Last year's runners-up took an early 4-0 lead over Andrew Reed's men after two ends, and maintained control throughout the contest, securing victory with two points in the ninth.
Having retained their position at the top of the rankings, Swedish skip Niklas Edin said: "We knew this was a game we were favourites to win, but we still had to do the job.
"We had a good enough start to be able to relax and after two ends we felt in cruise control."
Following defeat to Russia in their second match, defending champions Scotland returned to winning ways with a comfortable 9-3 triumph over the Netherlands.
The Scots took a commanding 5-0 lead after two ends to settle any nerves, and after securing victory to ensure they are among the top of the chasing pack, skip Ross Paterson expressed his delight at his team's performance.
He said: "That was an important bounce-back game. We put those boys under pressure, we managed to get an early lead and after that we controlled the game."
Switzerland also notched their third win in four with a 10-6 win over the Russians to keep themselves in the hunt for glory, with skip Yannick Schwaller playing a raise take-out in the fifth end to give his side a healthy, 8-2 lead.
Elsewhere, Germany fell to their second defeat with a 10-3 reverse at the hands of Italy, while Norway edged a closely-fought contest with Denmark 8-7.