Ebobisse's goal allowed the Timbers to snap a three-game winless streak in which they were 0-2-1.
Yimmi Chara was just inside midfield when he fed Ebobisse for a run toward the net. As Ebobisse closed in, he delivered a left-footed blast over the outreached left hand of FC Dallas goalkeeper Jimmy Maurer.
FC Dallas had a chance to knot the score in the 87th minute but Ricardo Pepi's header missed to the right.
FC Dallas dropped to 1-5-4 since routing Portland 4-1 at home on May 1.
FC Dallas is winless on the road this season, dropping the six matches by a cumulative 13-2.
Portland goalkeeper Steve Clark had two saves while FC Dallas counterpart Maurer made one.
The Timbers outshot FC Dallas 11-7 but both teams put just two on target.
The match was filled with opportunities by both squads over the first 80-plus minutes.
Pepi had chances in the 34th and 39th minutes, first failing to convert on a header and then drilling the right post with a right-footed shot.
FC Dallas had another solid opportunity in the 43rd minute but Paxton Pomykal's close-range left-footer was saved by Clark.
One minute later, Portland had a chance to break the scoreless tie but Dairon Asprilla's right-footer was saved by Maurer.
Three minutes into the second half, Chara of the Timbers had his right-footed shot miss to the left.
Asprilla had a solid opportunity in the 63rd minute but his header was just wide of the top right corner.
Chara had another chance in the 70th minute but his right-footer went right of the net.
One minute header, FC Dallas' Franco Jara sent a header wide to the right.
Portland's Diego Valeri delivered a right-footer in the 77th minute that sailed over the net.