Stanford plays in Bramlage Coliseum on the campus of Kansas State University (map) on Saturday, March 18th at 12:30pm local (Central) time.
Manhattan, KS is a two-plus hour drive from the nearest major airport, Kansas City (code MCI). In no case is it feasible to fly from SFO on the Saturday and reach Manhattan in time for the game. You must fly on Friday.
Update: Manhattan's local airport (code MHK) is served by American Eagle, a subsidiary of American. It is possible to book flights on American from SFO, changing in DFW, direct to MHK. The times are not any more convenient but the long drive from the bigger city is avoided. The rest of this post is based on flying into KC.
There is a single nonstop flight from SFO, UA5454, which uses quite a small plane, so is probably sold out by now. Other flights by United and American involve one change. If you catch an early (5am-7am) departure, you can arrive in KC early enough to make the drive to Manhattan on Friday evening. Be sure to notify your chosen hotel of late arrival.
What we have opted to do is to fly into KC and stay Friday night at the airport Marriott. On Saturday morning we'll make the drive to Manhattan early and stay in a hotel there for three nights.
The two-plus hour drive back to KC must affect your choice of return flights as well. Fortunately KC is a relatively compact airport. The rental car agencies are on the airport grounds, not a long bus ride away. But you'll want to depart Manhattan at least four hours before your scheduled departure. However, the weather forecast is for partly cloudy -- we should not have bad weather to contend with at either end of the weekend.
Remember that the FBC Travel page has many useful links for scheduling flights.