The buyer will get $1,000 off the purchase price and the Tesla owner who provides the referral will get a $1,000 credit toward a future car purchase, service charge or accessories, according to a letter that is going out to Tesla owners.
Prospective customers will be able to buy a new Model S online by clicking a link from a current Tesla owner.
Each Tesla owner can grant a maximum of 10 $1,000 discounts.
Prizes are part of the program, too. If five people order a Model S, the referrer and a guest will receive an invitation to tour Tesla's Gigafactory in Nevada and attend the grand-opening party.
At 10 orders, Tesla said the referrer gets the right to purchase a Founder Series Model X, which is not available to the public, with all options free.
In mid-July, Tesla CEO Elon Musk said the 2016 Tesla Model X midsize electric SUV is on track for the first deliveries in about two months.
Tesla's word-of-mouth discount program coincided with the release of a new Edmunds.com analysis Wednesday that said the automaker is poised to expand its reach beyond its traditional base of wealthy, trend-setting customers with the help of the used-car market.
The analysis examined registration data of all 1,600-plus Tesla Model S electric cars that have ever been sold in the U.S. pre-owned market.
A key finding: While only 25 percent of new Model S buyers earned less than $100,000 a year, that number rises to 36 percent of all used Model S buyers.
Used Model S buyers also skew younger than new Model S buyers. About 10 percent of pre-owned Model S buyers are millennials, age 18-34, compared to just 6 percent of all new Model S buyers.
"The used Model S data proves that with a more attainable price tag, there is demand for the vehicle from a more diverse customer set," said Edmunds.com Director of Industry Analysis Jessica Caldwell. "A wide-range buyer base is essential for a brand like Tesla that hopes to grow with mainstream shoppers."
Edmunds says: Own a Tesla? Know people who also want to own a Tesla? Well, you can now team up to reap valuable and exclusive rewards.