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Sagarin's Predictor ratings, in Sagarin terminology the best single predictor of future games, would park the spread at 26 points on a neutral venue. But since the team moved to the shady side, and dragged the students there too, Stanford Stadium has been far from a neutral venue.
So I will predict that Stanford extends the current 27 or more margin of victory run and wins by at least 28. 38-10
For the BCS beauty pageant this week's margin of victory actually is quite important. If Stanford "only" beats UCLA by 10 or so, then I would predict that a one loss Oklahoma team could join one loss SEC teams in the group that could pass undefeated Stanford in the final BCS rankings.
Since the Pac-12 is weak it is very important to look good when beating any Pac-12 team that lost to top AQ schools from other conferences. It is a sad system, but it is the system and style points matter.