Characterizing the global maximum of weighted sum-rate (WSR) for the K-user Gaussian interference channel (GIC), with the interference treated as Gaussian noise, is a key problem in wireless communication. However, due to users' mutual interference, this problem is in general non-convex and thus cannot be solved directly by conventional convex optimization techniques. In this paper, by jointly utilizing the monotonic optimization and rate profile techniques, we develop a new approach to obtain the globally optimal power control solution to the WSR maximization problem for the GIC with single-antenna transmitters and receivers. Different from prior work, this paper proposes to maximize the WSR in the achievable rate region of the GIC directly by exploiting the facts that the achievable rate region is a normal set and the users' WSR is a strictly increasing function over the rate region. Consequently, the WSR maximization problem belongs to the class of monotonic optimization over a normal set and thus can be solved globally optimally by the outer polyblock approximation algorithm. However, an essential step in this algorithm hinges on how to efficiently characterize the intersection point on the Pareto boundary of the achievable rate region with any prescribed rate profile vector. This paper shows that such a problem can be transformed into a sequence of signal-to- interference-plus-noise ratio (SINR) feasibility problems, which can be solved efficiently by existing techniques. Furthermore, this paper sheds some lights on how the proposed algorithm can be applied to solve WSR maximization problems for the multi-antenna GICs.