Two second-half goals in a five-minute period saw the Swans sink to a 3-2 defeat at Everton.
The Toffees had taken a 19th-minute lead through Leighton Baines' penalty after Ross Barkley went down under Chico Flores' challenge.
But the Swans reacted well to falling behind, and they were back on level terms after the half hour as Wilfried Bony tapped home Angel Rangel's low cross.
The Swans finished the half strongly, but they didn't show the same intent when the teams emerged after the break.
And Everton took full advantage as firstly Romelu Lukaku tapped home Kevin Mirallas' low cross after 53 minutes, and then Barkley nodded in from close range following a corner five minutes later.
Garry Monk's side had a string of chances following that, with Hernandez, substitute Michu and Rangel all failing to take advantage.
Ashley Williams headed home in added on time, which gave the Swans hope, but Everton held on for victory.
Defeat, and with other results going their way, meant the Swans remained four points clearof third-bottom Sunderland.
This loss, which meant the Swans are still searching for their first win over Everton, left the Swans on 29 points after 30 games and in 15th place.
The Swans made three changes to the starting XI.
Chico Flores returned from a one-match suspension while fellow Spaniard Pablo Hernandez came into midfield, while the final change saw Nathan Dyer start on the wing.
Jonjo Shelvey was among the substitutes as he returned from a hamstring problem, while Spanish international Michu hoped to build on his 30-minute appearance in last weekend's home defeat to West Brom.
EVERTON:Tim Howard (capt), Leighton Baines, Aiden McGeady (Leon Osman, 84), Kevin Mirallas, Sylvain Distin, James McCarthy, Romelu Lukaku (Gerard Deulofeu, 90), Gareth Barry, Ross Barkley (Steven Naismith, 84), Seamus Coleman, John Stones.
SUBS: Joel Robles, Luke Garbutt, Antolin Alcaraz, Tyias Browning.
SWANS: Michel Vorm, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton, Jose Canas (Jonathan de Guzman, 69), Pablo Hernandez, Nathan Dyer (Jonjo Shelvey, 62), Wayne Routledge, Wilfried Bony (Michu, 69).
SUBS: Gerhard Tremmel, Jordi Amat, Neil Taylor, Roland Lamah.
After the Swans had made a bright start, with Wilfried Bony shooting twice inside the opening 30 seconds, Everton imposed their authority on the game.
Seamus Coleman's cross failed to find a clean connection from Ross Barkley, before the latter earned the hosts a penalty after 19 minutes.
With the Swans pushing on, John Stones picked up possession and his crossfield pass found a gap in the Swans defence. Ross Barkley raced on and when he went down under Chico Flores' challenge, referee Michael Oliver pointed to the spot.
Up stepped Leighton Baines, and the left-back just beat Michel Vorm despite the Dutch keeper diving the right way.
The Swans needed a response, and they got one after 33 minutes.
Wayne Routledge cut inside and chipped into the box for Angel Rangel, and his superb first-touch allowed him to cross low to Bony, and he tapped home from two yards.
And the Swans looked to build on that goal as they went close to getting another.
Firstly, Nathan Dyer fired over after Davies broke before feeding Routlede, who teed up his fellow winger, and then Tim Howard had to be alert as he raced out to clear with Bony lurking.
Then, in added on time, a Pablo Hernandez free-kick was deflected just wide with Howard wrongfooted, before a Dyer volley following a corner was deflected wide as the Swans ended the half strongly.
HALF-TIME: Everton 1 Swans 1
Both sides went in search of the lead after the restart, and after the Swans saw Hernandez's chip easily collected by Howard, the hosts stepped up the pressure.
Lukaku saw his low effort kept out by Vorm, before the Dutch keeper reacted well again to deny the Belgian striker.
Then Everton took the lead in the 53rd minute as they punished the Swans for some sloppy play.
With the visitors making a swift counter attack, Hernandez raced on but a sliding challenge from Sylvain Distin stopped the Spaniard in his tracks.
Everton were immediately on the attack and when Lukaku spread play out to the right for Mirallas, his low cross found Lukaku, who tapped home from close range.
It got worse for the Swans five minutes later as Everton doubled their lead.
Mirallas' corner bounced in the box straight into the path of Ross Barkley, and the midfielder headed into the ground and into the net.
Garry Monk made his first change past the hour as Jonjo Shelvey replaced Dyer, which meant Hernandez moved out to the wing.
And the Spaniard made an instant impression out wide as his perfect cross found Bony in the box, but his leaping header was kept out by a fine reflex save by Howard.
Then Everton threatened via Mirallas, who pinched possession off Davies on the halfway line and raced in on goal, but his shot was saved by Vorm.
The Swans, though, created another fine chance as Bony's through ball sent Rangel in on goal, but the right-back's shot was blocked by the covering defence.
It prompted Monk to make a double change, with Jonathan de Guzman and Michu on for Jose Canas and Bony.
And Michu was straight into the centre of the action as Shelvey slipped in a pass for Michu, but when he shot on the turn an Everton defender was there to block it out for a corner.
Another opportunity came the Swans' way as another superb through ball from Shelvey found Hernandez in the box, but the Spaniard's effort was deflected wide by the knees of Howard.
Michu then headed wide from a Rangel cross as the Swans continued to push for a goal to get them back within touching distance.
And when Ashley Williams headed home Hernandez's corner into net via the crossbar in added on time, the away crowd had hope.
But the whistle blew soon after, which meant a second consecutive league defeat with a trip to Arsenal next on the agenda.