Despite losing for the seventh time in nine games, the Angels remained 15 games ahead in the West.
Perkins (11-3) held Los Angeles to five hits, struck out three and walked two on the way to winning his fourth consecutive decision. Dennys Reyes pitched the ninth to complete Minnesota's ninth shutout.
The Angels have been shut out six times.
Young hit a two-run homer off Joe Saunders in the fourth, and Span added a three-run shot against Shane Loux as the Twins broke the game open with a five-run sixth.
Saunders (14-6) allowed six runs and nine hits in 5 1-3 innings. He hasn't won since July 30, with three no-decisions and a loss over that stretch.
Span, who had four RBIs, made it 4-0 with two outs in the sixth with his third home run.
Young's two-run homer with two outs in the fourth gave Minnesota a 2-0 lead after both teams squandered early scoring chances. It was Young's eighth homer.
Span's RBI single in the fifth built the lead to three runs.
Notes: Mauer singled in the seventh to extend his career-high hitting streak to 14 games. ... The Twins have gone 42-19 since June 13, the most victories in either league during that span. ... Perkins threw 107 pitches, matching his high for the season.
