Over the last years, web browsing has been steadily shifting from desktop computers to mobile devices like smartphones and tablets. However, mobile browsers available today have mainly focused on performance rather than power consumption, although the battery life of a mobile device is one of the most important usability metrics. This is because many of these browsers have originated in the desktop domain and have been ported to the mobile domain. Such browsers have multiple power hungry components such as the rendering engine, and the JavaScript engine, and generate high workload without considering the capabilities and the power consumption characteristics of the underlying hardware platform. Also, the lack of coordination between a browser application and the power manager in the operating system (such as Android) results in poor power savings. In this paper, we propose a power manager that takes into account the internal state of a browser -that we refer to as a phase -and show with Google's Chrome running on Android that up to 57.4% more energy can be saved over Android's default power managers. We implemented and evaluated our technique on a heterogeneous multi-processing (HMP) ARM big.LITTLE platform such as the ones found in most modern smartphones.