Lionel Messi was the saviour for the Blaugrana once again, as he scored twice in the second half; Martin Braithwaite had a good game as well, bagging two assists.
Both sides made an enterprising start to the game, but the visitors would regret squandering an early chance when Lucas Boye blazed his effort over the woodwork.
In the 20th minute, Francisco Trincao missed a golden opportunity at the other end. He was brilliantly denied by Edgar Badia, who was moving the wrong way but stretched his other arm to palm away the shot.
Barcelona, in particular, struggled to break into the Elche box. The visitors were made to wait till the 43rd minute for their first shot on goal but the danger was comfortably averted by Marc Andre Ter Stegen.
Messi then delivered the opener, finding the back of the net just two minutes after the break. He linked up wonderfully with Brathwaite to beat Badia from close range.
The visitors responded almost instantly, but Boye messed up a first-time effort after a rare break. Thereafter, it was one-way traffic as Barcelona piled on the pressure.
Messi bagged his second of the night after converting Frenkie de Jong's pass. Five minutes later, Jordi Alba put the result beyond doubt for Barcelona by adding a third from close range. Messi set up Braithwaite, who headed the ball across to an unmarked Alba.
Despite the win, Barcelona remain third in the league standings, five points behind league leaders Atletico Madrid, having played a game more.
On that note, let's take a look at the five talking points from the game.
#5 Elche defensive approach against Barcelona backfires
Barcelona were frustrated by Elche in the first half, as the visitors' gritty defence denied the Blaugrana any goal-scoring opportunities.
Elche played a five-man defence for most of the game, as they went into half-time with the game goalless.
Edgar Badia was particularly in inspired form, denying Trincao twice from close range. However, after Barcelona opened the scoring in the second half, there was no looking back for the Blaugrana.
#4 Barcelona produce an improved second-half display
After a dull and soporific performance in the opening 45 minutes, Barcelona were in danger of a third disappointing result in a row at the Nou Camp.
Barcelona struggled to create chances in the first half and had nothing to show for bossing possession. However, things improved in the second half.
Messi led from the front. Given a free role in the changed formation, the Barcelona captain ran at the Elche defence and scored a wonderful goal after a quick one-two with Braithwaite.
That goal opened the floodgates for the hosts, who added two more before the final whistle to return to winning ways.