The Polish forward continued his sensational form since joining from Bayern Munich this summer, with a brace taking him to 11 goals in eight appearances across all competitions.
With Real Madrid, who boast a 100 per cent record after five games, visiting Atletico Madrid in the Sunday night capital derby clash, this was a chance for Barcelona to provisionally depose their rivals for the first time this season, and they took it.
Barca coach Xavi Hernandez rotated in midfield after the Champions League defeat by Bayern Munich on Tuesday, with Frenkie de Jong and Franck Kessie stepping in, while Memphis Depay was handed a rare start in attack.
Elche, bottom of the table, made the job significantly easier for the hosts when Gonzalo Verdu hauled down Lewandowski as he burst through on goal after 14 minutes and was swiftly dismissed.
Lewandowski, top of the division's scoring charts with eight goals, had been uncharacteristically profligate against his former club, but he did not extend that generosity to the visitors at Camp Nou.
Barcelona racked up the chances and inevitably Lewandowski broke the deadlock after 34 minutes.
Pedri set Alejanrdo Balde in down the left and the young defender cut a ball across the six-yard box for the veteran striker to simply cushion into the net.
Memphis doubled the lead with a sharp individual turn and powerful strike which flew past Edgar Badia, and Pedri added a third shortly before half-time but it was disallowed for offside.
Barcelona only had to wait three second half minutes for it, with Lewandowski pouncing on a loose ball in the box and finishing clinically to put the game far beyond Elche's reach.
After Cadiz's late win over Real Valladolid on Friday night, Francisco Rodriguez's side were left bottom of La Liga on one point, and never looked like changing it against Xavi's sparkling side.
Badia denied Lewandowski his hat-trick with a fine save and the striker fired fractionally over the bar before being replaced by Ferran Torres, to an ovation from home supporters already under his spell.