Dustin Jeffrey had two goals and Tyler Seguin, Ray Whitney and Ryan Garbutt also scored for the Stars, who have won five of their last six games as they make a push for their first postseason appearance in six seasons.
Dallas entered Tuesday one point behind Phoenix for the final wild card spot in the Western Conference. The Coyotes had a late game against Winnipeg.
The Stars ran their winning streak against the Capitals to five games.
Lehtonen had 12 saves in the first period, 10 in the second and 13 in the third for his 26th career shutout.
Jaroslav Halak gave up three goals on 23 shots in just under 30 minutes before he was pulled Braden Holtby, who allowed two on 13 shots.
The Capitals have lost four in a row. It was only the second time in their last nine games, though, that they didn't earn a point (4-2-3). They remain just outside playoff position in the Eastern Conference.