Goals from Vitolo, Carlos Bacca and Ivan Rakitic rewarded the hosts' dominance as they moved six points ahead of their opponents in the race for a European place.
Getafe lie ninth but could be overtaken by Espanyol should the Barcelona side win at Osasuna later in the day.
Sevilla threatened through two early headers, Vitolo denied by keeper Miguel Moya before Federico Fazio's effort went over.
Bacca's shot was also too high and Vitolo shot wide, either side of an optimistic effort from Getafe's Borja Fernandez.
Kevin Gameiro provided the most serious threat of the opening 20 minutes, Sevilla's French striker hitting a post with an angled drive.
Fernando Navarro's volley and Coke Andujar's drive both cleared the crossbar before the crucial moment of the first half arrived shortly after the half-hour.
Getafe went close when Adrian Colunga forced an excellent reaction save from home keeper Antonio Beto, but Sevilla broke away and within a minute had taken the lead. Bacca was the provider with a through-ball for Vitolo to finish neatly from six yards.
Getafe's search for an equaliser yielded only two unthreatening efforts from Sergio Escudero before the break, while Pedro Leon fired wide shortly after.
And Bacca put the game to bed 10 minutes into the second period when he met Fazio's cushioned header with a close-range volley into the bottom corner.
Colunga shot wide and Escudero fired over, while in between times Sevilla went close through Rakitic.
Getafe's challenge petered out completely, though, and after Bacca tested Moya and Daniel Carrico headed over, Sevilla added a deserved third goal in the 77th minute.
Bacca again provided the final pass for Rakitic to finish low from just inside the box.
Rakitic and Piotr Trochowski saw long-range shots saved by Moya before Marko Marin sent a late chance over the bar from close range.