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.
Antonio Conte's resurgent side wrapped the match up inside the first half, courtesy of an early Romelu Lukaku goal and a sensational strike by Khvicha Kvaratskhelia.
Victor Osimhen has been sidelined by Napoli after the team he fired to Serie A glory just a over year ago left him both off their squad list for the 2024/25 campaign and potentially in season-long limbo.
Belgium striker Lukaku completed a permanent move to Napoli from Chelsea on Thursday, ending a long period of limbo with the Blues.
The futures of Napoli striker Victor Osimhen and England international Ivan Toney are set to dominate the final day of the European transfer window on Friday as Chelsea continue their frenzied pursuit of new signings.
Napoli manager Antonio Conte apologised to the club's fans after his side were humbled 3-0 at Hellas Verona in Serie A on Sunday and said he took responsibility for the loss.
Napoli insisted on Monday Khvicha Kvaratskhelia is not for sale as the star Georgian winger's agent pushes for a move away from the Serie A club, reportedly to Paris Saint-Germain.
Former Chelsea and Tottenham coach Antonio Conte was hired by Napoli on Wednesday as the deposed Serie A champions try to bounce back from their disastrous league title defence.
Empoli, who are battling relegation, opened the scoring after four minutes when striker Alberto Cerri headed in a close-range cross for what proved to be the winner.
"We're not mathematically out of it but the chances of us getting there are very slim," said Calzona after his first league defeat as Napoli boss
Italian club Napoli said they were "stunned" after Italy's football federation (FIGC) on Tuesday dropped a probe into alleged racist comments made by Inter Milan's Francesco Acerbi to Napoli's Juan Jesus due to lack of evidence.
