Shaw placed third after the first two races on day one and improved two places to first as three outings were scheduled with the worst result so far discarded.
The 29-year-old's first race on day two became her discard as she finished 13th before bouncing back in style with back-to-back victories in her next two.
That saw Shaw jump up two places into the lead with ten points with France's Charline Picon second with 13 and Lee-El Korsiz another one back in third.
The gap to fourth is nine points while Shaw's British teammates Izzy Hamilton and Claudia Carney rank 18th and 30th overall respectively after five races with three more scheduled on day three.
Meanwhile in the men's fleet Nick Dempsey also jumped up the overall standings to third with a sixth and two seconds from his three races, his discard the seventh from race two on day one.
It's tight at the top with Greece's Byron Kokkalanis leading Olympic champion Dorian van Rijsselberge by one point with Dempsey level with Piotr Myszka in third another point back.
Elliot Carney is 24th overall and fellow Brit Tom Squires 27th and Dempsey admitted to being satisfied with his performances so far in Brazil.
"The weather was quite tricky again on the water and I had a six and two second places," he said. "That is not bad, the first result is a little bit disappointing, but the weather was quite difficult there, so, it's OK."
- Sports & Recreation
- Nick Dempsey