The record five-time winners had claimed a 1-0 first-leg victory in Rome last week thanks to a Ben Yedder strike, and the Frenchman doubled their overall lead on 20 minutes by tapping in after Pablo Sarabia’s shot was saved by Thomas Strakosha.
Ben Yedder has now scored 21 goals this season, including eight in the Europa League.
Franco Vazquez’s sending off on the hour mark gave Lazio hope of an unlikely comeback, but visiting midfielder Adam Marusic was also dismissed 11 minutes later.
Sarabia wrapped up a 3-0 aggregate success by lashing home Jesus Navas’ pass with 12 minutes to play.
Pablo Machin’s Sevilla, who sit fourth in La Liga in the race for Champions League qualification, are playing in Europe’s second-tier competition for the first time since winning their third straight title in 2015-16.
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