Swansea City lead Everton 1-0 at half time in their League Cup third-round encounter at the Liberty Stadium thanks to Nathan Dyer's 28th-minute strike.
Gylfi Sigurdsson had the first chance of the game for a dominant Swansea side as he curled a 20-yard effort just wide of the upright.
Everton slowly came back into the game though, and two of Roberto Martinez's summer signings almost combined for the opener, but Gerhard Tremmel denied Christian Atsu after the winger was played through on goal by a precise Samuel Eto'o pass.
Tim Howard then denied Jefferson Montero at the other end from a tight angle, before Tremmel was called into action twice more to deny Antolin Alcaraz and Aiden McGeady's tame efforts.
Just as Everton looked to be gaining a foothold in the game, Dyer connected with Montero's cross from close range to put the home side ahead after 28 minutes.
Everton looked to respond immediately and Muhamed Besic curled a shot wide before Ashley Williams deflected Atsu's strike behind as the home side held on until the break.
