Shaw, who finished seventh at London 2012 four years after taking bronze at Beijing 2008, began the RS:X regatta in America with a second and fifth on day one before a fifth and third on day two.
And the 29-year-old enjoyed her best outing yet on day three in Miami as she won the first race and fifth of the regatta overall before coming home second in the second.
British teammate Hamilton won the second race and sits sixth overall with Shaw now just one point off of Mexican Vega, who recorded two thirds, in second with 13 points.
Meanwhile in the men's RS:X fleet Nick Dempsey remains in third place after two fifths with Dorian van Rijsselberghe extending his lead by claiming victory in both races on day three.
Fellow Brit Elliot Carney sits fifth after a second in race one on the day and then a throw out in race two just six points behind third-placed Dempsey.
In the Laser fleet, Alex Mills Barton was fifth and fourth to place ninth overall while teammates Jack Wetherell is 25th and Matt Reid 36th after six races in Miami.
And in the 2.4mR class, Megan Pascoe remains in contention for overall victory, sitting joint second with Allan Leibel, just four points shy of Bruce Millar, after two second-place finishes.