Patrick Kane and Duncan Keith were on target as Chicago clinched the title at home for the first time since 1938.
It was the only match of the series not to be decided by a single goal.
Keith opened the scoring in the second period and was named most valuable player of the play-offs to deny Tampa in their first final since 2004.
Chicago Blackhawks claimed their third Stanley Cup in six years with a 2-0 win against Tampa Bay Lightning that gave them a 4-2 series victory.