The point allows FC Dallas (6-3-6) to climb into a second-place tie with Portland at 24 points, which trails top team Sporting Kansas City by three points.
Vancouver (6-6-2) is tied with San Jose for fifth place with 20 points.
Saturday's match was scoreless until FC Dallas forward Maximiliano Urruti scored at the 52-minute mark. He left-footed the ball past two defenders and goaltender David Ousted.
The goal, Urruti's eighth this season, is the first scored by FC Dallas at BC since the 2014 season.
Vancouver is 4-2-4 at home against FC Dallas.
Vancouver tied the match on midfielder Christian Techera's fourth goal of the season, a left-footed free kick at the 74-minute mark that escaped diving goaltender Jesse Gonzalez on the left side of the goal.
The free kick was a result of a foul by FC Dallas' Michael Barrios on an attacking Matias Laba.
FC Dallas' defense was mostly effective throughout, allowing only two shots on goal and six shots overall. Offensively, it was not opportunistic, failing to take advantage of four other shots on goal other than Urruti's score and 16 shots overall.
Ousted was busy most of the night, tallying four saves.
Vancouver is 4-1-1 in its last six matches at home. The Whitecaps entered Saturday's match winning four of their last five matches at BC Place.
FC Dallas, which played on only three days' rest after beating the Tulsa Roughnecks in a U.S. Open Cup game last Wednesday, next plays Friday at the Houston Dynamo.
Vancouver next plays at Minnesota United FC on Saturday.