Close-season signing Martins broke the deadlock after 33 minutes, the lively Portuguese winger bundling home after a quick team move that saw him break through the middle.
The Catalan minnows nearly produced a late equaliser, but goalkeeper Antonio Adan denied Elhadji Bandeh and Joan Noguera struck the crossbar.
Valencia's Santi Mina struck twice on his return from injury to help them avoid an embarrassing defeat at CD Ebro, as Marcelino's side came back to win 2-1.
The third division team had Tiago Portuga sent off after 29 minutes for two yellow cards but took the lead through Jon Ander just after the hour mark.
Mina, however, curled in a fine equaliser in the 71st minute, adding a second in the 80th to hand Los Che the advantage.
La Liga side Levante stumbled at second-tier Lugo, drawing 1-1, while Leganes fought back from two goals down to draw 2-2 with local rivals Rayo Vallecano.
Real Madrid head to Melilla on Wednesday and Cultural Leonesa host Barcelona. The second leg matches take place from Dec. 4-6. (Reporting by Rik Sharma Editing by Toby Davis)
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