Both quarterbacks threw for six touchdowns and combined for 1,064 yards, but Carr had his streak of interception-free passes end at 306.
That costly mistake, coming early in the fourth quarter, ended Fresno State's hopes for an unblemished campaign. The interception led to a San Jose State field goal that put the Spartans in front by 18 points with 4:46 to go.
Chandler Jones caught three of Fales' touchdown throws, one of them a 19-yarder that came with 18 seconds to play in the second quarter and gave San Jose State a 42-41 halftime lead.
The Spartans then limited Fresno State to 11 points over the final two periods.
Fresno State dropped to 10-1 for the season and is 7-1 in the Mountain West Conference's West Division.
Despite the loss, Fresno State will represent its division in the conference championship game. Utah State will be the opponent in that game if it can defeat Wyoming Saturday.
Fales completed 37-or-45 passes for 545 yards. Carr was 38-of-50 for 519.
Three of Carr's scoring throws went to Devante Adams, who piled up 264 receiving yards.
Fales' yardage total was the most for a Mountain West Conference quarterback this season, and with San Jose State reaching 6-6 for the year, the Spartans become bowl eligible.
San Jose State defeated a ranked team for the first time in 22 tries.