Tarvet, who came through three rounds of qualifying, thrilled a packed crowd around Court Four with a majestic display to outclass fellow-qualifier Riedi.
Second-round losers are guaranteed £99,000 in prize money, but because Tarvet is still a student at the University of San Diego, he will miss out on a potentially career-changing windfall.
Because of his amateur status, the world number 719 will be entitled to only $10,000 plus any expenses he incurs.
Although that will hurt in the short term, such was the quality of Tarvet's game that he looked destined for a rapid rise in the rankings and he will likely turn professional after his final year of study in California.
Tarvet was the only British player to survive the qualifying tournament, joining 22 other home players in the singles draws, 14 of them wildcards.