Youssef En-Nesyri won the points for Sevilla after nipping in at the near post to tap in Lucas Ocampos's low pull-back with seven minutes remaining in a match dominated by the reigning UEFA Europa League champion.
Julen Lopetegui's side is one point behind Real Madrid as it scopes a top-four spot and a return to Europe's elite competition for next season.
Sevilla also held a tribute to its former player Maradona, who signed for the Andalusian club in 1992 after the end of a long drugs ban which hastened his exit from Napoli. He stayed one season before returning to Argentina with Newell's Old Boys.
A minute's silence was held before kick-off in which the Sevilla players wore shirts with Maradona's number 10 on the back while the song My Dear Buenos Aires played over the loudspeaker.
Huesca remains 19th, level on seven points with bottom side Celta Vigo after failing to win a single match from its 11 so far.
In the early match, newly-promoted Elche and Cadiz shared the spoils in a 1-1 draw which continues their surprise starts to the season.