Eaks shot a 7-under 65 in the final round to finish with a 54-hole total of 193, four shots better than Ed Doughertys finish in 2000. Gary Hallberg and Bernhard Langer tied for second at 17-under 199 for the tournament.
Eaks, who had one top 10 finish in 14 previous events he completed this year, led by as many as six on the front nine at the TPC Twin Cities, but back-to-back birdies by Gene Jones cut the lead to two on 14.
Eaks second shot on the par-4 15th went through the green, but he regrouped and chipped in from deep rough for birdie.
Jones bogeyed 16 and double-bogeyed 17. He finished at 16 under, seven shots back.
Ron Streck (70) finished at 15 under, and Mike Goodes (66), Tom Kite (65) and Rod Spittle (65) finished at 14 under. Jones, Goodes and Spittle were Monday qualifiers.
Loren Roberts, who started the day three shots back, shot a 72 and finished 10 shots back.
Defending champion D.A. Weibring shot 68 in the final round to finish at 11 under. No champion has defended his title in the events 16-year history.