After the Preds had taken a 3-0 lead in the first period, the Blues peppered Rinne with 14 shots in each of the next two frames as they battled to get back into the game, but Finnish goalie was dented only once.
Brian Elliott started in net for St. Louis but was pulled in the second period after yielding four goals on 11 shots.
Rookie Jake Allen made his NHL debut in relief, stopping 6-of-8 shots the rest of the way as the Blues dropped a second straight.
Alex Pietrangelo notched the only goal for St. Louis.
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