When you access an article from a search, your search terms are highlighted, and your URL contains a question mark followed by a long mess.
For example: http://www.jstor.org/stable/20543113?seq=2&Search=yes&list=hide&searchUri=3Bq6%3Bf4%3Dall%26amp%3Bla%3D%26amp%3Bpt%3D%26amp%3Bf5%3Dall%26amp%3Bf0%3Dall%26amp%3Bwc%3Don&prevSearch=&resultsServiceName=null
To remove the highlighting, copy the URL just up to the question mark (the part in bold here). Don't copy the question mark itself.
You can also click on Email Citation to email the link to yourself. The citation sent includes the persistent link, which is listed as the Stable URL.