Enrique left the Nou Camp on a high after his side produced an accomplished display to clinch their third Copa del Rey title in a row.
Lionel Messi, Neymar and Paco Alcacer were all on target as Barca cruised to a routine victory.
Alves were so close to taking the lead in the 27th minute, but Ibai Gomez was denied by the woodwork.
Messi however calmed the nerves on the half hour mark when he played a one-two with Neymar and struck a first time shot from 20 yards into the top corner of the net.
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Lionel Messi scored his 54th goal of the campaign
It was his 54th strike of the season and also meant he became the first player to score in four different Spanish Cup finals.
Alaves were level in the 33rd minute when Theo Hernandez curled a stunning free-kick home from 25 yards.
Neymar doubled Barca’s advantage on the stroke of half-time when he tucked home from four yards out.
Neymar produced the goods once again in the Copa del Rey final
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The result was beyond doubt when Messi turned provider, as Alcacer scored from close range.
Enrique signed off as Barca boss with three Spanish cups.
During his three years in charge, he also won La Liga twice, the Champions League, the Fifa Club World Cup, Uefa Super Cup and Spanish Super Cup.