The win moved Napoli three points behind leaders Inter Milan, who beat Udinese 2-1, while third-placed Atalanta lost 1-0 at Fiorentina.
Antonio Conte's side are level on 61 points with reigning champions Inter after a largely lacklustre performance which with better finishing would have still been enough for victory on the Venetian Lagoon.
Antonio Conte's Napoli climbed back to within a point of leaders Inter Milan, who came from two goals down to beat bottom side Monza 3-2 on Saturday.
Reigning champions Inter could cut the gap back to three points when they host Fiorentina on Monday.
Belgium striker Lukaku nodded home his eighth Napoli goal from Andre-Frank Zambo Anguissa's perfect cross in the 78th minute to give Antonio Conte's team a statement win in Bergamo.
Georgia striker Khvicha Kvaratskhelia on Friday signed for Paris Saint-Germain for an undisclosed fee from Italian league leaders Napoli, the French champions announced.
Frank Anguissa and Amir Rrahmani scored Napoli's goals in an eight-minute spell in the first half before Andrea Pinamonti cut the deficit early in the second period.
Fiorentina earlier remained on Napoli's heels after their 1-0 home win over Cagliari in their first league match since midfielder Edoardo Bove's sudden collapse last weekend.
Lazio will face either Inter Milan or Udinese in the quarter-finals.
Barcelona came flying out of the blocks with goals from Fermin Lopez and Joao Cancelo but after Amir Rrahmani pulled one back, the Catalans started to sweat.
Nigeria forward Osimhen rolled home the leveller with 15 minutes left of the first leg of their Champions League last 16 tie at the Stadio Diego Armando Maradona, in his first match since returning from the Africa Cup of Nations.
The 62-year-old Mazzarri became the second man to be sent packing this season by the ailing Italian champions.
Nigeria striker Victor Osimhen will leave Napoli this summer and join "either Real Madrid, Paris Saint-Germain or an English club", the Italian club's president and owner Aurelio De Laurentiis said on Friday.
Napoli put aside their recent troubles on Thursday by reaching the Italian Super Cup final with a convincing 3-0 win over Fiorentina in Riyadh.
Napoli striker Victor Osimhen has replied angrily to suggestions that he would leave the Serie A side for Saudi Arabia at the end of this season from agent Mamuka Jugeli, who represents club team mate Khvicha Kvaratskhelia.
Italy's highest court cleared the late Agentine soccer legend Diego Maradona of tax evasion charges, ending a 30-year-long legal battle between the ex-Napoli striker and revenue authorities.
Defending Serie A champions Napoli saw their non-winning league ways continue Friday with a goalless draw against mid-table Monza.
Yann Bissek's first goal in Italy just before half-time at the San Siro and a late finish from Nicolo Barella were enough for Inter to bounce back from cup defeat to Bologna midweek and keep closest challengers Juventus at bay.
Victor Osimhen has signed a contract extension with Napoli until 2026, the Serie A champions announced on Saturday.
