The Barcelona midfielder has barely been used this season but put himself in the shop window with a confident display against the third-tier visitors in a comfortable round of 32 second-leg victory.
Holding a 1-0 first-leg lead Barcelona soon stretched that advantage, with Munir El Haddadi slamming a strike into the top corner after 18 minutes to complete a slick team move.
Suarez curled home a delightful second from distance to double the lead and Malcom headed in the third from Ivan Rakitic's cross.
The Croatian captained a much rotated side, with key players like Lionel Messi and Gerard Pique left out of the squad to rest for Saturday's Catalan derby against Espanyol.
Sene pulled a goal back from close range but highly-rated playmaker Riqui Puig appeared in the second half for his Barcelona debut and created the fourth goal with a sweet dink that Suarez dispatched coolly.
The only blemish for Barca came when Brazilian winger Malcolm appeared to suffer a late injury and was taken off, amid an injury crisis at the club with Luis Suarez, Samuel Umtiti and Sergi Roberto among players sidelined.
Barcelona, who have won the competition a record 30 times and for the last four seasons, will be joined in the next round by Real Sociedad, who knocked out Celta Vigo 3-1 on aggregate after a 2-0 win.
Villarreal thrashed Almeria 8-0 (11-3) to progress with striker Karl Toko Ekambi scoring four, while Sevilla edged past Villanovense 1-0 (1-0) thanks to Andre Silva's 49th minute strike and Real Valladolid beat Mallorca 2-1 (4-2).
Atletico Madrid hammered Sant Andreu 4-0 (5-0), while Girona came from behind to beat Alaves 2-1 (4-3). (Reporting by Rik Sharma, editing by Ed Osmond)
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