Strategy against a MUCH stronger player

My inflation-adjusted $0.02, if you are playing to win the game:  Play to make the game last as long as possible. 

My rationale:  Any game that's supposed to be a mis-match where the heavy favorite has to play late into the round carries a psychological boost for the underdog, the longer the game goes.  If you're one of the later games going, you will be able to feel the energy as onlookers start to encircle your table.  What's better, you can safely know that most of them will be rooting for you to win (as many people like watching upsets).  Finally, the more moves you make, the more chances you'll have for the higher rated player to teach you something new.

Practical application:  Play an opening you know (even if you think the higher rated player knows it better).  Keep material level, and try to avoid long-term positional weaknesses (backward pawns, open files that you can't contest, etc.) - higher rated players love to get their hands on one or two of those weaknesses, and then they can squeeze you for a while without risking much.  Manage your time well - leave plenty of time to work out complicated middlegame and endgame issues.  In many such upsets, the clock becomes a factor, because the higher rated player will burn time looking for the pretty win that isn't there, while the lower rated player will play simple, practical moves.

A few additional comments:  If you attack, do so VERY selectively.  Sometimes, the position simply requires aggressive play...but you can usually do this without torching all your bridges.  (In concert with this, I'd avoid certain all-or-nothing openings.  An extreme example:  the Latvian Gambit.)

As a director, I've had the opportunity to witness a fair number of heavy upsets first-hand.  The factors I've laid out above don't necessarily all apply to every such upset.  However, most of them appear in most of the really big upsets you see.