Nigeria forward Osimhen rolled home the leveller with 15 minutes left of the first leg at the Stadio Diego Armando Maradona in his first match since returning from the African Cup of Nations.
The 25-year-old equalised Robert Lewandowski's 60th-minute opener, which seemed likely to be the decisive goal as Barca were for long periods the better team. Even so, it was his team's first shot on target.
Osimhen had last played for Napoli in a 2-0 defeat at Roma just before Christmas, when he was one of two players from his team to be sent off.
His ninth club goal of the season came at a crucial time, not just in the match but in Napoli's campaign as they play under their third manager of the season in Francesco Calzona.