Sevilla lifted the trophy in 2007 and 2010 and unlike many other La Liga teams in this round of a much-maligned competition, they fielded an almost full-strength side at the Sanchez Pizjuan.
Federico Fazio headed in a corner after three minutes and the visitors levelled in the 70th following a brilliant run and shot from Christian Alfonso.
"The best thing about the game is the result," Sevilla coach Michel told a news conference. "We can play much better than this."
Last season's runners-up Athletic Bilbao could only manage a 0-0 draw at neighbours Eibar of the Segunda B on a rain-soaked, churned-up pitch.
"Melilla were intense and more competitive," said Levante coach Juan Ignacio Martinez. "We need to make sure we never underestimate anyone and we must always keep our focus."
In Thursday's late game Manuel Pablo's fizzing long-distance volley for Deportivo La Coruna was cancelled out by Pedro Geromel's back-post header for Real Mallorca, leaving the sides level at 1-1 ahead of the return leg in Palma next month.
