He was the American League's Most Valuable Player and Cy Young Award winner in 1992, a season in which he posted 51 saves. Only two relievers had previously accomplished the double feat: Rollie Fingers in and Willie Hernández in . Since Eckersley, one other reliever, Éric Gagné, has won Cy Young honors (Gagné won the National League award in with the Los Angeles Dodgers). In the 1992 American League Championship Series against the Toronto Blue Jays, during Game 4 in what some considered the turning point in the series that the Jays won, Eckersley gave up a game-tying 2-run home run to Roberto Alomar and his team eventually lost 7–6 in 11 innings.