Sampdoria slid into Italy's Serie B on Monday as they lost 2-0 away to Udinese while Empoli held their nerve to beat Salernitana 2-1 to pull away from the relegation zone.
Sampdoria are last in Serie A on just 17 points, 13 from safety with four games left.
Roberto Pereyra put the hosts ahead after nine minutes running onto a pass by Festy Ebosele and clipping the ball over the diving Nicola Ravaglia.
Adam Masina scored the second with a header from the penalty spot after 34 minutes.
Empoli meanwhile pulled 11 points clear of danger and leapfrogged the team they beat, Salernitana.
Nicolo Cambiaghi put them ahead with a diving header after 37 minutes.
Francesco Caputo added a second in the 63rd minute. Finding himself alone in front of goal following a corner, he stepped round goalie Guillermo Ochoa and smacked the ball into the empty net.
Substitute Krzysztof Piatek pounced on a rebound in the 86th minute to give the visitors hope.
But the nearest either team came to scoring in the dying minutes was a ferocious strike by Empoli's Marco Pjaca, disallowed after a video review because team-mate Razvan Marin was offside.
Sampdoria meanwhile dropped out of Serie A after 11 years following a disastrous season, on and off the field.
Things could grow worse for the Genoese club as they face possible further relegations because of financial problems.
The club has struggled to pay its bills and only avoided a points deduction by convincing the players to give up December's salaries.
Massimo Ferrero, who had to resign from the presidency in December 2021 after being arrested in a case of fraudulent bankruptcy but remained the club owner, might be ready to sell, Italian media have reported.
The 71-year-old film producer has owned Sampdoria since 2014.
In February, a box with a pig's head was left at the club's headquarters with a threatening message for Ferrero and vice-chairman Antonio Romei.
Sampdoria's rival and co-tenant at the Luigi Ferraris Stadium, Genoa secured promotion back to the Italian top flight on Saturday.
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