The Blues forced Vancouver to earn at least a point in its game against Edmonton later Saturday to finish with the best record in the Western Conference. A Vancouver loss in regulation to the Oilers would give St. Louis the No. 1 seed in the conference.
Perron's goal gave the Blues a 3-1 lead and the insurance score turned out to be vital when Philip Larsen tipped in a shot for Dallas with 3:04 remaining.
Jaroslav Halak picked up the victory with his 33 saves. Richard Bachman stopped 32-of-35 shots.
St. Louis had lost four consecutive games coming into its concluding contest of the regular season.
Dallas let an excellent chance at the playoffs get away by losing seven of its last nine games and its last five in a row. Before the late slump the Stars had owned the lead in the Pacific Division.