Lewandowski scored in either half and has now registered 11 goals in eight appearances in all competitions since joining Barca from Bayern Munich in the summer.
Memphis Depay also scored his first goal for the Catalans following his arrival from Lyon in July.
Depay’s strike was sandwiched by Lewandowski’s brace, with Elche failing to trouble Xavi’s side after skipper Gonzalo Verdu’s early dismissal for hauling down the Poland striker.
Barca sit one point above Real Madrid, who play at city rivals Atletico on Sunday.
Athletic Bilbao held on to beat Rayo Vallecano 3-2 at home and climb up to third place in the table.
After Oscar Trejo had given the visitors an early lead, Inaki Williams, Ohian Sancet and Nico Williams put Athletic in control and they held on despite Radamel Falcao’s late effort.
Samu Castillejo, Marcos Andre and Andre Almeida were on target for Valencia in a 3-0 win against Celta Vigo, which lifted them to within a point of the top six.
Mallorca bounced back from last week’s 4-1 defeat at Real by defeating Almeria 1-0 at home, thanks to Pablo Maffeo’s first-half header.
Bayern Munich slipped to their first defeat of the season in the Bundesliga, losing 1-0 at Augsburg, and could slide out of the top four by the end of the weekend.
Mergim Berisha’s solitary strike halted a run of three straight home defeats for Augsburg as they recorded their first home win of the season and extended Bayern’s winless league run to four matches.
Borussia Dortmund climbed top the table with a 1-0 home victory against derby rivals Schalke, with teenage substitute Youssoufa Moukoko heading a late winner.
Borussia Monchengladbach climbed into the top six after beating RB Leipzig 3-0 at home. Germany midfielder Jonas Hofmann fired a first-half double and Ramy Bensebaini completed the scoring.
Eintracht Frankfurt sit a point behind in seventh following their 3-1 win at Stuttgart, where Sebastian Rode, Daichi Kamada and Kristijan Jakic were on target for the visitors. Tiago Tomas replied for the hosts.
Milos Veljkovic’s late equaliser salvaged Werder Bremen a 1-1 draw at Bayer Leverkusen, who had led through Kerem Demirbay, and the point was enough to lift the home side out of the bottom three.
In Serie A, Agustin Alvarez’s stoppage-time header clinched Sassuolo their first away win of the season, 1-0 at Torino, who have lost three of their last four matches.
Empoli registered their first league win of the season as Filippo Bandinelli scored the game’s only goal at Bologna and winless Sampdoria remain in the bottom three after losing 2-1 at Spezia.
In Ligue 1, Lille moved up to sixth after beating Toulouse 2-1 at home and Strasbourg’s winless run was extended to eight matches as they went down by the same scoreline at Montpellier.