Chicago moved into the Eastern Conference finals with a 3-2 aggregate margin in the two playoff games with United.
Barrett scored in the 31st minute and Rolfe produced a goal two minutes later by sneaking between two defenders deep in the box and putting a volley past goalkeeper Troy Perkins.
Now holding a 3-0 advantage in the series, the Fire settled into a defensive mode in the second half and had to fight off a United comeback. Clyde Simms scored in the 69th minute and Christian Gomez in the 74th.
With the home crowd chanting and waving flags, United attacked time and again during the closing minutes. An apparent United goal in extra time by Christian Gomez was waved off because of a handball violation.
Chicago will meet the winner of the New York-New England matchup in the conference finals.