The Argentina striker struck to cancel out Iker Muniain's first-half strike and set up an intriguing second leg in Spain.
Iker Muniain put the La Liga side in front just before halftime and it looked to be on its way to an impressive win, only for Higuain to level in the 68th minute.
The two sides meet again in Spain on Aug. 27 with all to play for as they bid to reach the group stages of Europe's elite competition.
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Both teams had opportunities inside the opening 10 minutes, with Marek Hamsik heading over a Higuain cross from a central position before firing over the bar after good work from Lorenzo Insigne.
But it was the visitors who took the lead in the 42nd minute when Muniain fired home into the bottom right-hand corner after being fed by Oscar De Marcos.
Athletic could well have extended its lead early in the second period, with Arturo Ardiz going close with a left-footed effort 49 minutes in.
Napoli had little in the way of scoring opportunities but found itself back on level terms in the 68th minute as Hamsik supplied Higuain, who duly found the back of the net to make it 1-1.
The result gives the Spanish side a slight edge heading into the second leg, which takes place at San Mames.