It needed a special strike from Federico Dimarco in the second half to break down Empoli's resolute defence, which had conceded 12 goals in their previous four matches.
More than half of those came in last weekend's 7-0 defeat at Roma, which led to the dismissal of coach Paolo Zanetti and the hiring of Aurelio Andreazzoli for his third spell at the club.
Inter have now won all five of their Serie A matches, conceding just one goal, and moved three points ahead of second-place AC Milan.
Defending champion Napoli are already seven points behind Inter after a 0-0 draw at Bologna.
Inter traveled to Empoli full of confidence after last weekend's 5-1 thrashing of Milan in the city derby.
The Nerazzurri piled on the pressure from the start and had two good opportunities in the opening two minutes, while Matteo Darmian's header had to be headed off the line by Empoli defender Ardian Ismajli in the 10th minute.
Inter thought it had broken the deadlock in the 35th but Marcus Thuram's goal was ruled out for offside.
The visitors did finally make the breakthrough six minutes into the second half. An Inter corner was headed out but only as far as Dimarco on the edge of the area and he unleashed a precise shot on the half-volley into the top far corner.
Rudi Garcia's job could be at risk only a few months into his tenure as Napoli coach.
Garcia took over in June after the resignation of Luciano Spalletti, who had just ended Napoli's 33-year wait for the Serie A title.
But Napoli are now winless in their past three league matches.
Victor Osimhen should have given Napoli the lead with 18 minutes remaining but he fired a penalty wide of the right post.
Osimhen had also hit the post early on.
Garcia was jeered by Napoli fans when he substituted Khvicha Kvaratskhelia and later Osimhen. There were also loud jeers at the end of the match.
Romelu Lukaku struck again but Roma were held to a 1-1 draw at Torino and only have one win in five league matches.
Lukaku's goal — following a good team move in the 68th minute — was his third in four matches.
Duván Zapata leveled for Torino with five minutes remaining when he headed in a free kick. Zapata almost joined Roma in the offseason from Atalanta.
Claudio Ranieri's Cagliari are still looking for their first win back in Serie A after they lost 2-0 at Atalanta.
Goals from Ademola Lookman and Mario Pašalić secured Atalanta their third win of the season.
Lookman almost scored before his 33rd minute opener as he slalomed through the Cagliari defence but his strike came off the crossbar and seconds later, as the move continued, Davide Zappacosta also hit the right post.
Cagliari also saw an effort come off the woodwork nine minutes from time as they tried to get back into the match.
Elsewhere, clinical Fiorentina had two shots on target and scored from both as they beat Udinese 2-0. Udinese, who have only scored once in five matches, had 20 attempts on goal, eight on target.
