Swansea hit back to level from 2-0 and 3-2 down at Anfield, before Henderson finally killed off their resistance in the 74th minute to take Liverpool back to within four points of leaders Chelsea.

It was a 10th consecutive home league win for Liverpool and gave Brendan Rodgers's side a provisional six-point lead over fifth-place Tottenham Hotspur, who visit Norwich City later on Sunday.

Liverpool needed less than three minutes to take the lead, with Sturridge collecting Raheem Sterling's pass and rounding Swansea goalkeeper Michel Vorm to score after Angel Rangel had lost possession in midfield.

Sturridge has now scored in eight consecutive Premier League games and he set up his side's second goal in the 20th minute with a lay-off that was curled home by Henderson.

Two goals in four minutes brought Swansea level, however, with former Liverpool midfielder Jonjo Shelvey smashing home via the crossbar before Wilfried Bony headed home via a deflection off Martin Skrtel.

Sturridge restored Liverpool's lead in the 36th minute, converting a cross from Luis Suarez with his head, but Bony equalised from the penalty spot early in the second half after he had been pulled back by Skrtel.

It had been a ramshackle performance by Liverpool, but they finally secured victory with 16 minutes remaining when Henderson bundled the ball home after Suarez's shot was deflected into his path.

In the day's other game, Loic Remy marked his return to the Newcastle United team after suspension by smashing home an injury-time winner in a 1-0 victory over Aston Villa.

The French striker collected a deflected effort by Luuk de Jong and beat Villa goalkeeper Brad Guzan in the 92nd minute to give Newcastle a first home win in five league games after a run of four straight defeats.