You can install the Sublime Text plugin BrowserRefresh-Sublime. From the README:
After installing this plugin you can hit command+shift+r on Mac OS X or ctrl+shift+r on Windows and Linux while using your favorite browser, the last active window will come to the foreground (you can turn this off in Chrome, Canary, Safari, WebKit and Yandex on Mac) and reload the active tab. If the current file is unsaved, it will be saved before the browser is activated and reloaded.