The Citroen driver ended the 2.47-mile test close to Hagfors four tenths of a second faster than Volkswagen's Jari-Matti Latvala.
Ostberg was fastest through much of the morning, but remained cautious about the impact of possible condition changes.
"It's good," Ostberg reflected after shakedown, "but now we have to see what the weather is going to be doing."
Kubica says Sweden was valuable
The unseasonably warm weather left many of the drivers taking a much steadier approach to shakedown in an effort to save their studded tyres, after gravel began to break through the icy surface.
VW's reigning World Rally champion Sebastien Ogier deployed such tactics and ended the session a lowly 12th fastest.
Ostberg's team-mate Kris Meeke was third fastest despite going off the road on his second run.
Returning Norwegian star Henning Solberg was immediately on the pace, fourth fastest in his Ford Fiesta and one place ahead of Hyundai's Thierry Neuville.
Irishman Craig Breen overcame illness to claim sixth quickest in his Fiesta RS WRC, 2.6s down on Ostberg's benchmark.
Juho Hanninen (Hyundai i20 WRC) was seventh, while M-Sport's Robert Kubica wound up ninth after electing to take it slowly through his third and fourth runs at the test.
Marcus Gronholm's verdict on Robert Kubica
The Pole's team-mates Elfyn Evans and Mikko Hirvonen both took a similar approach and ended the 23rd and 28th respectively.
Sweden win key to Latvala title bid
Latvala leads, Mikkelsen closes in