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 half-time and they looked to be on their way to an impressive win, only for Higuain to level on 68 minutes.
The two sides meet again in Spain on August 27 with all to play for as they bid to reach the group stages of Europe's elite competition.
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 on 42 minutes when Muniain fired home into the bottom right-hand corner after being fed by Oscar De Marcos.
Athletic could well have extended their 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 goalscoring opportunities but found themselves back on level terms on 68 minutes as Hamsik supplied Higuain inside the area, 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 a week on Wednesday at San Mames.