Freshman Joey McKenna finished second at 141 pounds in the Defense Soap & Flips Wrestling Southern Scuffle in Chattanooga, Tenn., while four other Cardinal placed in the tournament.
Stanford finished ninth with 59.5 points. Penn State won the team title with 183 points, followed by Oklahoma State (158) and Lehigh (104.5).
Tied 1-1 after regulation, McKenna was called for a stalling point in the first tiebreaker which proved to be the difference for Heil, who was able to ride out McKenna in the second tiebreaker.
McKenna is just the second Cardinal wrestler to reach the finals of the Southern Scuffle, joining three-time All-American Tanner Gardner who did so in 2006. The rookie is 11-1 on the season.
Redshirt freshman Paul Fox (149 pounds) and redshirt sophomore Nathan Butler (285 pounds) finished seventh, while redshirt sophomores Connor Schram (125 pounds) and Garet Krohn (184 pounds) took eighth.
Stanford hosts Cal Baptist on Saturday at 2 p.m.