Villarreal started well and thought that they had made the breakthrough in the early exchanges through Yeremy Pino, but the attacker's goal was disallowed due to an offside.
Instead, it was Barcelona that went 1-0 up in the 20th minute, with Lewandowski sweeping an excellent pass from Pablo Torre into the back of the net, with Villarreal made to pay by the experienced marksmen.
Lewandowski had a second in the 35th minute, with the striker expertly turning home from close range after Eric Garcia had seen his header from a Lamine Yamal cross kept out by Villarreal goalkeeper Diego Conde.
Villarreal had one back in the 38th minute, though, with Ayoze Perez turning into the back of the net after Nicolas Pepe had picked out his teammate with a pass.
Ter Stegen then had to be stretchered off the field after landing awkwardly, and there are now fears that the goalkeeper could be set for a lengthy spell on the sidelines with a serious knee injury.
Barcelona were able to overcome the incident to score a third in the 58th minute through Torre, with the midfielder finding the corner from just outside the box, before Lewandowski smashed a penalty against the post in the 66th minute, as Villarreal continued to look shaky at the back.
The Yellow Submarine were ultimately unable to stem the flow of traffic, as Barcelona, who added a fourth and fifth late on through Raphinha, continued their perfect start to their 2024-25 La Liga campaign, moving onto 18 points in the table, four ahead of second-placed Real Madrid.
VILLARREAL VS. BARCELONA HIGHLIGHTS
20th min: Villarreal 0-1 Barcelona (Robert Lewandowski)
Barcelona make the breakthrough in the 20th minute of the contest, and it is Lewandowski with the goal; Torre's excellent pass finds Lewandowski inside the penalty box, and the striker fires into the back of the net.
35th min: Villarreal 0-2 Barcelona (Robert Lewandowski)
Lewandowski scores his second of the match, with the Poland international converting from close range with a clever over-head kick after Garcia's header had been kept out by the Villarreal goalkeeper.
38th min: Villarreal 1-2 Barcelona (Ayoze Perez)
Villarreal halve the deficit in the 40th minute of the match, and it is Perez on the scoresheet; Pepe breaks into a dangerous area and squares it to the Spaniard, who simply could not miss.
58th min: Villarreal 1-3 Barcelona (Pablo Torre)
Barcelona score a third just before the hour, and it is a brilliant goal from Torre, who finds space on the edge of the penalty box before curling his effort into the corner of the net.
75th min: Villarreal 1-4 Barcelona (Raphinha)
Barcelona score a fourth in the 75th minute of the contest, with Raphinha's effort from inside the box taking a deflection before ending up in the back of the net; Barcelona have made sure of all the points.
83rd min: Villarreal 1-5 Barcelona (Raphinha)
Raphinha has his second and Barcelona have their fifth - what a performance!
The Brazilian races onto a pass from Yamal before bouncing the ball over the onrushing goalkeeper.
MAN OF THE MATCH - ROBERT LEWANDOWSKI
Lewandowski passed up the chance to complete his hat trick from the penalty spot, hitting the post in the 66th minute, but it was still a brilliant performance from the striker.
The 36-year-old scored two brilliant goals to send Barcelona two goals ahead, and he was a constant threat in the final third of the field, demonstrating that he is still one of the leading forwards in world football.
Lewandowski has now scored six La Liga goals this season in six appearances.
VILLARREAL VS. BARCELONA MATCH STATS
Possession: Villarreal 36%-64% Barcelona
Shots: Villarreal 13-17 Barcelona
Shots on target: Villarreal 4-10 Barcelona
Corners: Villarreal 7-3 Barcelona
Fouls: Villarreal 12-12 Barcelona
BEST STATS
WHAT NEXT?
Barcelona will attempt to make it seven straight league wins at the start of the 2024-25 campaign when they welcome Getafe on Wednesday night.
Villarreal, meanwhile, will aim to bounce back from their first defeat of the season when they head to Espanyol on Thursday night.