The Catalan giants have endured a tricky start to 2015, with the fallout from Lionel Messi's dropping to the bench compounding the misery caused by Sunday's La Liga defeat to Real Sociedad.
Amid speculation over Messi's future at the club, the departures of former sporting director Andoni Zubizarreta and club favourite Carles Puyol, who served as his assistant, increased tensions around Barcelona.
However, coach Luis Enrique saw his side sweep aside Elche in the first leg of their cup meeting to put one foot in the quarter-finals of the competition.
Having initially been well marshalled by the Elche backline, Barca found a way through 34 minutes in when Neymar finished from close range.
Seemingly taking heart from their lead, Barca turned on the style and added two more goals before the break courtesy of Luis Suarez and a Messi penalty.
Jordi Alba made it four early in the second half before Neymar added his second in the 59th minute to complete the scoring on a comfortable outing for captain Messi and his colleagues.
With the likes of Messi and Neymar restored to the starting XI, Barca started brightly and made much of the early running, albeit without forging clear-cut chances.
That was until Messi jinked through the Elche defence and fired straight at Przemyslaw Tyton after 10 minutes.
Dani Alves then went close with a long-range effort after Titon elected to punch Messi's inswinging free-kick, while Neymar dinked Messi's lofted pass wide of the Elche goal before the half-hour mark.
Elche were seemingly coping well with Barca's threat, but they were eventually undone when Neymar finished off a neat passing move.
Suarez was the man to assist - squaring for the Brazilian to break the deadlock and open his Copa account for the season.
And Suarez added a second five minutes later, the Uruguayan cleverly dummying a ball from Alves to bamboozle his marker before firing past Titon.
Things got worse for Elche prior to half-time as Enzo Roco brought down Neymar in the area - allowing Messi to tuck home a third.
It took the hosts just 10 minutes of the second half to extend their lead, Alba applying the finish following Messi's pass out wide, and Neymar then scored arguably the goal of the game with a long-range strike that took a slight deflection on its way in.
With any hopes Elche had of staying in the tie seemingly dashed, Barca opted to replace the Brazilian with Pedro following a strong challenge on Neymar from Damian Suarez.
The goals dried up for the home side after Neymar's second but the damage had already been done, with Luis Enrique's men all but certain to progress to the quarter-finals.
Elsewhere, Sevilla hold the upper hand in their tie with Granada after a 2-1 first-leg win at Estadio Nuevo Los Carmenes.
