Slapdash win keeps Liverpool in the hunt
Liverpool striker Daniel Sturridge (L) celebrates scoring his team's third goal with Jordan Henderson during their English Premier League football match against Swansea in Liverpool on February 23, 2014 - by Andrew Yates
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.
"The strong part of our game came through," said Rodgers.
"Our offensive game is very aggressive and we've got goals in the team, but we're disappointed with the goals we conceded.
"We're just focused on winning games and no-one's really talking about us for the title; everything's about Chelsea, (Manchester) City and Arsenal. We'll just try to continue to improve."
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 a shot in off 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 fouled 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 claiming an injury-time winner in a 1-0 victory over Aston Villa.
The French striker collected a deflected effort from Luuk de Jong and fired home in the 92nd minute to give Newcastle a first home win in five league games after a run of four straight defeats.
Victory lifted Alan Pardew's side above Southampton and into eight place, while Villa remain 13th.