Liverpool largely dominated the encounter and took a 2-0 lead after Dejan Lovren was left unmarked to steer home the opener and Henderson bent the ball into the top corner from 30 metres to put the visitors in command at halftime.
Chelsea fought back after the break when Diego Costa sidefooted home from close range after 61 minutes, but there was little further goalmouth action as the Reds comfortably held on.
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The win moved Liverpool level with Chelsea on 10 points after five games and prevented the Londoners from going top of the table.
After an important victory, Liverpool boss was full of praise for his team, who have already played Arsenal, Tottenham and Chelsea away from home in their first five fixtures of the season. "We played football like hell," said Klopp. "It was really nice to watch. In the second half it was a bit more difficult. After their goal, we managed it well."
Liverpool were sharper from the start than Antonio Conte's Chelsea, who seemed content to sit deep and invite pressure from the visitors, who happily set up camp in the hosts' half in the opening stages.
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Daniel Sturridge threatened after only two minutes, curling a shot from the edge of the area that slipped from keeper Thibaut Courtois's grasp and almost trickled over the line, but it was not long before Liverpool grabbed the lead.
Typically of a sluggish Chelsea performance, Liverpool opened the scoring by catching the hosts napping at the back.
A free kick found its way to Philippe Coutinho and his deep cross found four Liverpool players unmarked at the far post, with Lovren applying a cool side-footed finish past Courtois.
Rather than prompt a Chelsea response, the hosts seemed to retreat further into their shell, making sporadic forays upfield but rarely threatening Liverpool's goal.
Henderson's stunning second arrived after 36 minutes and was a fully deserved reflection of Liverpool's first-half dominance. Gary Cahill cleared the ball to Henderson 30 metres from goal and he took aim before curling beautifully into the top corner.
Having been completely outplayed in the first half, Chelsea briefly came out fighting after the break and pulled themselves back into the game on 61 minutes when Costa grabbed his fifth Premier League goal of the season.
Nemanja Matic, anonymous in the first half, did brilliantly to carry the ball to the byline and pull back for Costa to sidefoot past Simon Mignolet and wake the home crowd.
The striker then had a great chance to level four minutes later, swivelling on the ball before shooting straight at Mignolet from 15 metres, but if Chelsea were hoping to lay siege to the Liverpool goal in the closing stages, it never materialised.
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