The Liverpool midfielder claimed his second goal of the game by converting at the second attempt after Luis Suarez’s shot had been deflected into his path by visiting captain Ashley Williams.
Daniel Sturridge (in pic) also scored twice, while Swansea responded impressively with a brace from Wilfried Bony and a goal from Liverpool old boy Jonjo Shelvey seeing them level the game at 2-2 and 3-3.
An entertaining first half featured five goals in the opening 36 minutes and left Liverpool in command, although far from convincing, as they took a 3-2 lead into the half-time break.
The three goals also took Liverpool’s tally of first-half league goals this season to an astonishing 46 — 16 more than free-scoring Manchester City — but it was to Swansea’s credit that they refused to be swept aside.
Liverpool struck after barely three minutes as Sturridge wrote himself into the Premier League history books, becoming just the second player, after Manchester United’s Ruud van Nistelrooy, to score in eight consecutive games.
It was a fittingly memorable goal, as Raheem Sterling pounced on a loose pass from Angel Rangel and produced a magnificent through ball that allowed Sturridge to round advancing goalkeeper Michel Vorm and score.
Sterling forced Vorm into a diving stop soon after, but Liverpool’s anxious play in defence was already becoming evident by the time Henderson doubled the lead after 20 minutes.
The Swansea defence backed off, allowing Sturridge to cut in purposefully from the right and play a short pass to Henderson, who planted an unstoppable finish past Vorm from just outside the area.
It had the makings of a comfortable afternoon for Liverpool in their continuing attempts to finish in the Champions League places, but three minutes later Swansea were back in the game.
Escaping the attention of Liverpool’s markers, Nathan Dyer moved into a central position from the right wing before teeing up Shelvey to unleash a finish almost identical to Henderson’s in its power and accuracy.
Worse would follow for the home side four minutes later, although in controversial circumstances after Martin Skrtel was judged to have brought down Shelvey 30 yards from goal.
Jonathan de Guzman took the resulting free-kick and found Bony, who guided a header past Simon Mignolet via a helpful deflection off Skrtel.
Anfield was anxious but Liverpool resilient and by the 36th minute they were back in front after a long and patient build-up around the edge of the area.
Eventually, Suarez emerged on the left side of the Swansea box, picking out Sturridge with a far-post cross that the forward headed in from six yards.
Suarez, with a bold chip from the halfway line, might have added to the advantage, although threatening low shots from Bony and Dyer before the interval hinted that the outcome was far from settled.
Sure enough, within two minutes of the restart Swansea were level again, this time from a penalty conceded after Skrtel leapt with Bony to compete for Dyer’s cross and fouled the striker in the process.
Bony himself took the penalty and comprehensively beat Mignolet with a fierce finish into the bottom-left corner.
Suarez was then denied by Vorm’s sharp reflexes, while De Guzman placed a 20-yard free-kick just wide of the home goal and was thwarted by Mignolet after a neat back-heel from Bony.
Liverpool continued to threaten through Sturridge and Suarez, but it was Henderson who settled matters and the hosts might even have had a late fourth goal had Steven Gerrard’s shot not hit the post.
Results at a glance
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