Logano had briefly surrendered the lead after the final restart but stormed back, bumping Martin out of the way and grabbing the lead for good with four laps to go.
He ended 1 second in front, laying claim to his Sprint Cup first victory since a rain-shortened June 2009 race at New Hampshire and becoming this year's only driver to start on the pole and win.
Logano's Joe Gibbs Racing teammate Denny Hamlin rounded out the Top 5.
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