Cal senior had been tied for fifth following opening round.
Cal senior seven shots off pace of second-round leader Kyle Westmoreland.
Cal senior three shots off the pace of first-round leader Tim Crouch.
Kim was the 2012-13 unanimous national player of the year in men's collegiate golf.
Homa ties for sixth on final leaderboard to earn exemption until the third periodic re-order of 2014 Web.com Tour.
Homa heads into final 18 holes tied for ninth, while Kim is tied for 17th.
Homa heads into final 36 holes tied for fifth, while Kim is tied for seventh.
Kim fires six-under par 66 on Saturday, while Homa shoots a five-under 67.
Homa jumps up 77 spots into a seventh-place tie, while Kim moves up one into a tie for 14th.
Kim tied for 15th and Homa tied for 84th following Thursday's first round.
Cal junior was the unanimous 2012-13 national player of the year in men's collegiate golf.
2014 Palmer Cup slated to take place June 26-28 in England.