Russell gave Kansas City the lead in the 81st minute on a night the Galaxy lost MLS goal scoring leader Javier "Chicharito" Hernandez to a late injury scratch.
Shelton then added a goal in the fifth minute of second-half stoppage time as LA was caught pushing for an equalizer, in a victory that pushed Kansas City even on points with Seattle atop the Western Conference standings.
Seattle leads SKC on the first tiebreaker of goal differential.
Tim Melia made seven saves in Kansas City's third consecutive victory and first shutout of the season.
Jonathan Bond made four saves for the Galaxy, which held out Chicharito as a precaution because of a minor calf injury that crept up during warm-ups.
Samuel Grandsir led the hosts with three shots on target but fell short in the search for his first MLS goal.
After scoring 25 times in his first three MLS seasons, the Scottish international Russell entered Sunday without a goal despite 20 shots and five efforts on target.
He corrected that on a sequence that came largely against the run of play, when Felipe Hernandez forced a turnover deep in LA's own half.
Russell was first to the loose ball and struck an initial attempt denied by Bond. He then reached the rebound while it was still in the air and flicked a clever header that looped over the 'keeper and down across the line.
Shelton made it 2-0 on a breakaway when he beat Sacha Kljestan to a loose ball near midfield and, with LA pushing numbers forward, rounded Bond and tucked the ball into an empty net.
Melia's heroics before that helped keep KC in position to sneak out with a win.
His best stops may have come in succession in the 33rd and 34th minute, when he smothered Ethan Zubak's header off a dangerous set piece and then got just enough of Grandsir's attempt.