Coach Arne Slot’s team has 15 points after 6 matches, one point behind Manchester City Arsenal, and Wolverhampton ranks 20th with one point.
Konate opened the scoring in stoppage time of the first half, after Diogo Jota overtook his opponent on the left side and then sent an accurate cross, which the 25-year-old centre-back received with his head into the net.
Wolverhampton took advantage of a defensive error to equalize in the 56th minute.
Algerian record Rayan Ait Nouri The goal was from close range, after a joint error between Konate and goalkeeper Alisson Becker in clearing the ball, and Mario Lemina intervened with them and passed the ball to Nouri, who put it into the net.
And shut up Salah Wolverhampton fans at Molineux Stadium after another 5 minutes, when Liverpool won a penalty kick due to Nelson Semedo’s foul on Jota.
Liverpool had more chances in the final minutes, including a corner kick that Konate headed over the crossbar, and a shot into the bottom corner from Curtis Jones after exchanging passes with Salah, but the Wolverhampton goalkeeper stood guard.
Liverpool’s victory comes in light of a busy schedule, as coach Slot’s team crushed West Ham United 5-1 in the third round of the League Cup on Wednesday, while hosting Bologna in the Champions League 4 days later.
The struggling Wolverhampton, led by Gary O’Neill, have not been able to keep a clean sheet in 18 matches, since their 1-0 victory over Sheffield United last February.