Defender Andre Dias scored against the run of play with a superb volley from a free-kick after 27 minutes.
Sampdoria also won 1-0 away at Cesena with a last-gasp goal but dropped talisman Antonio Cassano after he swore at the club president last week.
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While Samp were getting used to the possible prolonged absence of Cassano, Fiorentina were welcoming back fan favourite Adrian Mutu from a nine-month drugs ban but his side could only draw 0-0 at Catania.
AC Milan's 2-1 defeat by Juventus on Saturday meant Lazio, relegation candidates last term, would stay top whatever the result in Sicily, but they still threw bodies in the way of practically every shot Palermo could muster.
Argentine playmaker Javier Pastore had missed a good early chance for the hosts and almost scored when Lazio goalkeeper Fernando Muslera struck a clearance against him.
Palermo piled on the pressure again in the second half after Lazio's Giuseppe Biava was dismissed for a second yellow card after 77 minutes, but Muslera and his defence held out to leave the visitors on 22 points from nine games.
Second-placed Inter Milan won 1-0 at Genoa on Friday.
"We still lack 18 points to reach the famous 40 mark and maybe safety (from relegation), and once we reach that we'll see," Lazio's cautious coach, Edy Reja, told Sky.
Next weekend Lazio face city rivals AS Roma, who will be without captain Francesco Totti after he was sent off in the 2-0 win over Lecce on Saturday.
NAPOLI FIFTH
While Lazio hope to sustain an unlikely title challenge with a modest squad, Sampdoria are poised to play without banished Cassano for the foreseeable future.
They missed his creative ideas in victory at Cesena, where Giampaolo Pazzini grabbed the winner in stoppage time.
Cassano, who had appeared to have outgrown his bad-boy image, was dropped and disciplinary proceedings were brought against him after he insulted club president Riccardo Garrone.
The Italy forward, whose Azzurri future is also unclear if he does not play, has apologised, but whether he will be sold in January or brought back into the fold remains to be seen.
Cassano has occasionally been compared to Diego Maradona, given their gifts and flaws, but to Napoli fans no one will come close to the Argentina great.
Maradona's former club celebrated his 50th birthday this weekend with a 1-0 win at Brescia, where Argentine striker Ezequiel Lavezzi fittingly grabbed the second-
