With this victory, Barcelona is one step closer to winning the 27th title in the Spanish Football League.
Barcelona raised its tally to 82 points from 33 games, extending the lead to 14 points with second-placed Real Madrid, who will play later Tuesday with fourth-placed Real Sociedad.
Osasuna defender Jorge Herando was sent off for a foul on Pedri in the middle of the first half.
But Osasuna managed to hold out until the 85th minute when Robert Lewandowski sent a cross to Frenkie de Jong, who headed it to Alba, so the latter fired it with his left foot into the net.
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