Celta dominated throughout, and Larrivey opened the scoring after a team move in the 27th before nodding in a rebound of Manuel "Nolito" Agudo's strike in the 83rd.
Goalkeeper Diego Marino then let Alex Lopez's seemingly routine shot slip through his hands in injury time.
With six goals this season Larrivey is the league's joint-fourth leading scorer.
Alcaraz replaced Jose Mendilibar, who was fired this week with the team in second-to-last place.
Levante showed no improvement and failed to add to a league-low four goals through nine rounds, three of which came in a 3-3 draw at Eibar.
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