Dawkins got his first goal of the season 2 minutes into injury time, breaking a 1-1 tie with a diving header on a pass from Steven Beitashour.
Wondolowski netted an insurance goal a minute later, collecting his MLS-best eighth of the season on a shot from inside Real Salt Lake's penalty box.
Khari Stephenson also scored for San Jose (5-1-1), which bypassed RSL (5-3-0) for first place in the Western Conference.
Kyle Beckerman found the net for Salt Lake.
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