Depends on what you mean by 'big game.' Our last win vs a top 5 opponent was Black 41 Flash Reverse Pass against Oklahoma in '01. Since then, we are 0-9.
In 2010, we beat #7 Missouri, a game in which Helu broke the single game rushing record, and I think it still stands to this day.
In 2011, we beat #9 Michigan State and #12 Penn State. That year also included a 27 point comeback against unranked Ohio State.
In 2012, we beat #20 Michigan.
In 2013, we beat #23 Georgia, a team that included Todd Gurley.
In 2015, we beat undefeated #6/7 Michigan State. Probably the biggest upset win this program has had since beating #4 Texas in 1960
In 2016, we beat #22 Oregon. This is probably our last big win, though the win over Michigan State last year was nice.