In his first post-season start, Odom shutout the Detroit Tigers, holding them to just three hits in the second game of the 1972 American League Championship Series to give Oakland a 2–0 series lead. The Tigers came back to tie the series as Odom took the mound for game five of the ALCS. He held the Tigers to just one unearned run in five innings, and Vida Blue pitched the final four innings as the A's beat the Tigers 2–1.