The touchdown came after the Vandals (6-7, 3-5 WAC) blocked a field goal attempt by the Spartans' Harrison Waid as time ran out in regulation to send the game into extra play.
Waid kicked a 39-yard field goal to give the Spartans (1-12, 0-8) a 23-20 lead in the OT period but the Vandals responded with the TD.
Enderle finished throwing 16 for 30 for 250 yards. Greenwood led Idaho in receiving with four catches for 86 yards while Troy Vital led on the ground with 76 yards.
Idaho took its first lead of the game when Justin Veltung scored off a 37-yard run with 14:50 left in the fourth quarter to give the Vandals a 17-13 lead.
Trey Farquhar added a 32-yard field goal with 7:14 to go, giving Idaho a 20-13 lead.
SJSU's Ryan Otten snagged a 6-yard pass from La Secla with 4:35 left to tie the game at 20.
The Spartans put up 496 yards of offense to Idaho's 421, but Waid proved to be the difference. He missed an extra point attempt in the third quarter could have won the game in regulation if his attempted wasn't blocked.