Padron, who completed 13 of 33 passes with an interception, got off to a successful start in his quest to become the second straight SMU transfer to star at QB for the Eagles. Bo Levi Mitchell led them to the FCS national championship in 2010 and won the Walter Payton Award as the division's top player last year.
Padron, who started 21 games for SMU from 2009-11, hit Jake Whitnell with a 3-yard TD pass in the second quarter to give Eastern Washington a 10-3 lead. Quincy Forte ran for 66 yards and a score.
It was the Eagles' first victory against an FBS school since an 8-5 win at Idaho in 2003.
Najee Lovett had eight receptions for 105 yards for the Vandals, who went 2-10 last season.
Although transfer Dominique Blackman won Idaho's starting QB job, he did not play Thursday. Logan Bushnell started and was 10 of 24 for 123 yards and an interception.
Copyright 2012 The Associated Press.