The most daring and acrobatic figure in Sochi this week isn't a snowboarder; it is Vladimir Putin, whose death-defying geopolitical gamble is the hottest game in town. With more twists and turns than a bobsled race, more fancy footwork than a figure-skating final and more dips and flips than a mogul run, Russian diplomacy is a dazzling spectacle these days—and despite his considerable handicaps, Mr. Putin is skating rings around his clumsy and clueless opponents in Washington and Brussels.

The Russian president's biggest...