Rangers recorded a first victory of the season over Alloa, who remain in the relegation play-off place with no wins in their last eight league games.
Nicky Law's 10th goal of the season proved to be crucial as Rangers maintained their pursuit of Hearts.
In often tricky conditions, Kenny McDowall's side could and should have scored more.
But Alloa themselves had opportunities to score and threatened to further dent Rangers' promotion push.
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