An Eder penalty put the hosts ahead in the 16th minute, and when the visitors' Brazilian midfielder Allan was dismissed for a second yellow card 10 minutes before the break their chances looked bleak.
Eder added a second two minutes into the second half to put Sampdoria in total control, but Udinese were given a lifeline just after the hour when Roberto Soriano was dismissed for the hosts.
However, in the 69th minute Francesco Guidolin's side were dealt a further blow when they were reduced to nine men following Gabriel Silva's sending off, the first time three players have been sent off for two yellow cards in the Italian top flight since October 1997.
Sampdoria put their numerical advantage to good use as they dominated the remainder of the game and added a late third thanks to Daniele Gastaldello as Udinese suffered a third consecutive league defeat.
Inter missed the chance to return to winning ways as they were held to a 1-1 draw by a resolute Chievo at San Siro.
The visitors took a surprise lead in the eighth minute through Alberto Paloschi, only for Yuto Nagamoto to bring Walter Mazzarri's side level four minutes later with his fifth league goal of the campaign.
Inter dominated the proceedings thereafter but were left frustrated as Christian Puggioni kept out what attacks they were able to create.
Chievo did threaten on the counter attack but were also wasteful in the attacking third, with Cyril Thereau sending their best chance well wide of goal.
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