UPDATE 3-Google's Q4 results shine after ad rate decline slows

* Shares climb after-hours on strong results * Core revenue, costs-per-click surpass expectations * International markets grow, holiday season helps By Alexei Oreskovic SAN FRANCISCO, Jan 22 (Reuters) - Revenue from Google Inc's core Internet business outpaced many analysts' expectations during the crucial holiday quarter and advertising rates fell less than in previous periods, pushing its shares up more than 4 percent. The world's largest Internet search company introduc