Full-back Stephan Lichtsteiner struck the decisive goal as Conte supervised his team on a match day for the first time since he was banned from the dugout for his alleged involvement in match-fixing.
Lichtsteiner's goal arrived five minutes into the second half and Palermo played the last 15 minutes with 10 men after Michel Morganella saw red after picking up two bookings.
Inter moved into second place, and above Napoli, with a 2-1 win at San Siro.
Fredy Guarin (eight) and Diego Milito (39) got the goals for Andrea Stramaccioni's side, who were grateful for a profligate Napoli performance.
Edinson Cavani did get a goal back for the guests on 54 minutes, but a leveller never materialised to relinquish second spot.
AC Milan continued their resurgence with an eye-catching 4-2 win on the road at Torino. Successive wins over Juve and Catania had lightened the mood in the Milan camp after a dismal start, and Sunday's convincing victory means Massimiliano Allegri's men are now well involved in the pack jostling for the European places.
Milan's victory came the hard way after they fell behind to a Mario Santana strike, but four unanswered goals from Robinho, Antonio Nocerino, Giampaolo Pazzini and Stephan El Shaarawy took the game away from the hosts.
Rolando Bianchi added a second for Torino with 10 minutes remaining.
Two second-half goals lifted Pescara off the foot of the Serie A table with a 2-0 win over free-falling Genoa. The injury-hit visitors hit the woodwork twice in the first half but their horror run continued as Vladimir Weiss set-up both Elvis Abbruscato and Ante Vukusic.
Victory was a first in five game in all competitions for Pescara, lifting them up to 18th and above Genoa who have now won just once in nine.
Pescara's success meant Siena went bottom after they relinquished a half-time lead to lose 3-1 to Catania. Alessandro Rosina opened the scoring on 10 minutes and while Catania laid siege on the home goal they were not level until five minutes after the break through Lucas Castro.
Gonzalo Bergessio then bagged a brace to pile more pressure on Siena.
Chievo relied on a pair of goals after the break, with Alberto Paloschi and Cyril Thereau on target, to grab their second away league win 2-0 at Cagliari.