Liverpool s Egyptian striker #11 Mohamed Salah runs with the ball during the English Premier League football match between Wolverhampton Wanderers and Liverpool at the Molineux stadium in Wolverhampton, central England on September 16, 2023. AFP
Hwang Hee-chan put the home side ahead early against their sluggish opponents at Molineux and they had a succession of chances to extend their lead in a sparkling first-half performance.
But Liverpool flew out after the restart and equalised through Cody Gakpo 10 minutes into the second period.
Jurgen Klopp's men pinned Wolves back from long periods and got their reward when Andy Robertson finished neatly in the 85th minute before an own goal from Hugo Bueno added gloss to the scoreline.
Liverpool's fourth straight win lifts them to the top of the Premier League ahead of the 1400 GMT kick-offs.
Wolves have struggled to find a cutting edge this season but they started brightly, with Pedro Neto and new-signing Jean-Ricner Bellegarde a constant threat.
They got an early reward when Neto drove down the left, danced through Liverpool's defence and crossed from the byline, finding Hwang, who finished crisply past goalkeeper Alisson Becker from an angle.
The high-energy home side looked dangerous every time they flew forward, with Liverpool, missing the suspended Virgil van Dijk and the injured Trent Alexander-Arnold, failing to exert any meaningful control.
But Wolves' incisive approach play was not matched by the quality of finishing and they squandered a number of inviting opportunities to extend their lead.
Defender Craig Dawson headed over from a corner at the back post.
Brazilian forward Matheus Cunha missed a glorious chance in the 34th minute after more brilliant work from Neto, mistiming his jump horribly.
Liverpool created a number of chances towards the end of the first half, hinting at the threat in their ranks.
Klopp brought on Luis Diaz for Argentine midfielder Alexis Mac Allister at half time and the Colombian came close to equalising with a header in the opening moments.
The German manager prepared to bring on Harvey Elliott and Darwin Nunez for Gakpo and Diogo Jota but Gakpo found time to level with his final touch.
Mohamed Salah, who had largely been kept quiet, received the ball on the right and fizzed it across the area, with Gakpo on hand to poke home.
Liverpool had a golden chance to take the lead when Diaz found Nunez in front of goal but his shot was saved by Jose Sa.
Klopp's men were pinning Wolves back and took the lead in the 85th minute when Robertson collected a poor clearance from Sa in midfield.
The Scotland defender drove forward, playing a one-two with Salah before finishing from close range.
Liverpool still had time for a third goal when Elliot's shot took a significant deflection off Bueno to beat Sa.
According to Opta stats, Salah has been directly involved in 200 goals (139 goals, 61 assists) in 223 games for Liverpool in the Premier League, with only Thierry Henry reaching this milestone in fewer appearances for a single club in the competition (206 games for Arsenal).
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