Goals from Danny Graham and Chico looked set to give the victory to Michael Laudrup's side, who lost to the Colorado Rapids before beating Ventura County Fusion in their two previous two tour matches.
However, San Jose substitute Steven Lenhart netted twice in the final 10 minutes to salvage a draw for the home side.
Both sides created chances to open the scoring at Buck Shaw Stadium before Graham managed to do so in the 41st minute when he took advantage of a defensive error to calmly beat home goalkeeper David Bingham.
Swans custodian Michel Vorm kept his side in the lead with a fine save to deny Sercan Guvenisik during a period of pressure from the home side at the start of the second half.
The Barclays Premier League side withstood that spell though and netted their second goal on the hour mark when summer signing Chico headed home his first goal for the club following a cross from centre-back partner Ashley Williams.
That looked set to give Swansea the win, but they were hit with by a late double by Lenhart.
San Jose pulled a goal back with 10 minutes left when Lenhart turned in a cross from fellow replacement Shea Salinas, and the striker then levelled up the scores with another header in the 85th minute as honours were shared.