Probably the last game that was bigger or at least similar was November 28, 2014 when they were #13 and playing at #11 Arizona for a spot in the PAC12 championship game.
That's similar stakes as this one, and that ASU was better ...but with playoff expansion, this Saturday probably edges out that game. And it was on the road as well (though Arizona obviously isn't far for ASU fans).
December 7, 2013 they had a game that was definitely bigger (they were #11 and playing #7 Stanford in the PAC12 CCG), but it also wasn't at home
Last time they played a game bigger than this in Tempe was November 22, 2007 when #7 ASU welcomed #11 USC to town with two weeks left in the season.
Side note - ASU lost all three of the games mentioned here