An usual front-line from Barca had La Masia products Abde Ezzalzouli and Ferran Jutlga ably line up alongside Ousmane Dembele due to Memphis Depay's injury and Sergio Aguero's retirement.
It looked like a master-stroke two minutes from the start after Jutlga took one touch from Gavi's forward pass to find target, but it was disallowed for offside.
Jutlga made sure at the second time of asking when he jumped high in the six-yard area with 16 minutes played to head in Dembele's corner-kick.
The second followed two minutes later after Gavi sliced through the defence following a pass from Clement Lenglet to go and beat goalkeeper Edgar Badia from the edge of the area.
Barca could've gone in to at halftime with a three-goal advantage from a ball through the middle seconds to the interval, but Gavi had his low strike in the area cleared off the goal-line.
The Blaugrana still probed with over ten minutes played in the second half when Jutlga managed to come short from a low pass to put Badia to work with the follow-up hoofed.
Elche, who up until this point saw little openings, received a lifeline inside 61 minutes after Tete Morente showed up unmarked at the far post and nestled the top corner.
It was all square within two minutes when Pere Milla attacked a surging ball from the right-side to head in from the far post amidst a scrambling Marc-Andre Ter Stegen.
Through it all, the Blaugrana should've been ahead again straight thereafter through a ball in the area but Jutlga went over after he managed to beat the offside trap.
As Riqui Puig and Nicolas Gonzalez entered, Barca reclaimed advantage five minutes from time through a cracking near corner finish from the self-same Gonzalez to get his side back on the winning trail.