"We'll sleep as leaders for the first time in two years," said Barca coach Xavi Hernandez. "We've done our homework and got the three points. We're on the right path."
Xavi 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. 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.
"We knew he would score goals and make the difference, but the personal side of him has surprised me," said Xavi.
"He has a lot of humility, commitment, hunger. He's very hard working."
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 Barca.
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.
Long after Lewandowski had been replaced, his name continued to ring around the stadium. In the forward, Barcelona finally have a player to replace Lionel Messi's goal contributions and help them compete for the title again, which they last won in 2019.
Lewandowski's arrival and the club's summer signings spree have given supporters a reason to watch again, as the 85,000 strong crowd testified to, compared to last season's languishing attendances.
"The excitement of the fans is palpable, in the stadium, in the streets, you have to maintain this hope and belief," added Xavi.
"The people are connected, Barcelona's support is more alive than ever."
Elsewhere, Ernesto Valverde's Athletic Bilbao moved up to third in the table after beating Rayo Vallecano 3-2 in an entertaining clash at San Mames.
Inaki Williams levelled for Athletic after veteran midfielder Oscar Trejo opened the scoring for the visitors.
Oihan Sancet and Nico Williams, fresh from his call-up to Luis Enrique's Spain squad for the upcoming Nations League clashes, netted to give the hosts a two goal lead in Bilbao.
Radamel Falcao pulled one back late on but Valverde's side held out for the victory, moving three points behind Barcelona.
Valencia thrashed Celta Vigo 3-0 at Mestalla to move eighth as Uruguayan striker Edinson Cavani made his debut following his move from Manchester United.
Gennaro Gatuso's team have a 100 per cent home record and played with conviction.
Samu Castellejo broke the deadlock in the first half, before Celta's Franco Cervi was sent off for a rash tackle on Thierry Correia.
Marcos Andre and Andre Almeida added late goals to wrap up the win.