This paper tests for the existence of an order effect in competitive situations using the natural experiment of the introduction of the “away-goals rule” in CONMEBOL club competitions. This rule states that in a case of a two-legged fixture finishing level on goals, the team that scores more goals as a visitor will qualify for the next round. Fixed-effects logit analyses for the period 1988-2014 provide evidence that, after the application of the rule in 2005, teams that played the second leg as visitors had an increased probability of winning in regulation time. This phenomenon was especially significant when the “visitor in the second leg” was the stronger team of an evenly matched game, or conceded no goals in the first match. Several explanations related to behavioral biases, such as psychological pressure, time inconsistency, and loss aversion, are proposed.