With the score tied 1-1, Diaz pounded home a cross from Fabian Castillo for the go-ahead tally.
Dallas defender Jair Benitez assured the outcome with an arcing shot from 50 yards out that cleared the reach of Whitecaps goalkeeper David Ousted in the 90th minute.
Dallas (10-7-11), which began the night in seventh place in the Western Conference, notched its first home win since May 25.
Vancouver (10-10-8) got a goal from Kenny Miller.
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