Garry Monk tasted defeat as head coach for the first time as the Swans' FA Cup hopes ended in the fifth round after Everton ran out 3-1 victors at Goodison Park.
The Swans found themselves a goal behind after just four minutes as Lacina Traore slotted home on his debut.
But Jonathan de Guzman's header from a Neil Taylor cross put the Swans back on level terms in the 14th minute.
Both sides had their fair share of chances for the remainder of the half, but it was the introduction of Steven Naismith which swung the tie in Everton's favour.
Just five minutes after being sent on, the Scottish international intercepted Neil Taylor's pass back and slotted home under Gerhard Tremmel.
Naismith then won a penalty for the hosts just minutes later as he went down under Jazz Richards' challenge, and Leighton Baines sent Tremmel the wrong way from the spot.
The Swans made eight changes to the starting XI.
Gerhard Tremmel started in goal while Jazz Richards made his first appearance since the Europa League qualifier against Malmo in Sweden.
Neil Taylor captained the side while Jordi Amat and Kyle Bartley - involved for the first time since last February's league defeat at Liverpool - were partnered in central defence.
Jonathan de Guzman went into midfield while Roland Lamah got the nod out wide. Up front, Alvaro Vazquez - who started the fourth-round win over Birmingham City - led the line.
Leroy Lita was among the substitutes as he looked to make his first appearance since the league draw at Bolton in April 2012. He was joined by club record signing Wilfried Bony and skipper Ashley Williams.
Garry Monk was without the rested Ben Davies and Angel Rangel while Chico Flores had a slight knee problem. Jonjo Shelvey, Alejandro Pozuelo and Michu remained sidelined through injury.
EVERTON:Joel Robles, Seamus Coleman, Leighton Baines, Phil Jagielka (capt), Sylvain Distin, James McCarthy, Gareth Barry, Kevin Mirallas (Gerard Deulofeu, 89), Steven Pienaar, Ross Barkley (Leon Osman, 60), Lacina Traore (Steven Naismith, 60).
SUBS: Tim Howard, John Stones, Tony Hibbert, Aiden McGeady.
SWANS: Gerhard Tremmel, Jazz Richards, Kyle Bartley (Ashley Williams, 30), Jordi Amat, Neil Taylor (capt), Jose Canas, Jonathan de Guzman, Pablo Hernandez, Wayne Routledge (Nathan Dyer, ht), Roland Lamah (Leroy Lita, 68), Alvaro Vazquez.
SUBS: Michel Vorm, Dwight Tiendalli, Leon Britton, Wilfried Bony.
The Swans were quick out of the blocks, and with just over 60 seconds on the clock a finely-threaded pass from Pablo Hernandez sent Alvaro Vazquez in on goal. The Spaniard beat the onrushing Joel Robles, but when he took the ball out wide, the covering defence got back in time to block Roland Lamah's effort.
But, as the Swans were kicking themselves for not being a goal ahead, they were soon a goal down.
In the fourth minute, Sylvain Distin nodded down a free-kick into the Swans box, and debutant Lacina Traore sidefooted into the net from six yards following Steven Pienaar's neat pass.
The Toffees pushed for another goal, but it was the Swans who got back on level terms on 15 minutes.
Neil Taylor's fine cross found Jonathan de Guzman, who had raced into the box, and the Dutchman headed home into the side of the net.
It proved an intriguing start, and the third goal of the game almost arrived with just over 20 minutes on the clock.
It was a major scare for the Swans as Pienaar connected with Ross Barkley's low cross, and when the ball hit the crossbar and post, Traore headed the loose towards the top corner. But it took an outstanding leaping save from Gerhard Tremmel to deny the striker.
The hosts probed again, but Tremmel was untroubled as Kevin Mirallas scuffed wide from a Seamus Coleman cross.
The Swans were forced into a change before the half-hour mark as Ashley Williams replaced Kyle Bartley, who had suffered a hamstring injury.
Both sides continued to push for the lead, and Tremmel saw off efforts from Kevin Mirallas and Ross Barkley, while he did well to spring across goal to punch away a Mirallas free-kick.
At the other end, Vazquez's lob drifted well wide despite beating Phil Jagielka to Wayne Routledge's ball over the top, while Lamah saw his volley easily collected low down by Robles as the whistle blew on an entertaining first half.
HALF-TIME: Everton 1 Swans 1
The Swans made a change at half-time as Nathan Dyer came on in place of Routledge.
And, after Barkley had seen his low driven shot saved by Tremmel, Everton made a double change as Steven Naismith and Leon Osman replaced Traore and Barkley on the hour mark.
And Naismith had an immediate impact as his flick on from Seamus Coleman's cross found Pienaar at the back post, but his header flew just wide.
But, on 65 minutes, Everton did take their chance as Neil Taylor's attempted pass back to Tremmel was intercepted by Naismith, and the substitute slotted home under the advancing keeper.
It could have got worse for the Swans as Mirallas got onto the end of a cross in the box, but the winger fired high over the crossbar from 12 yards out.
Garry Monk the introduced Leroy Lita as his final change, with the Swans going in search of an equaliser.
But Everton put themselves clear soon after, with Naismith going down under a challenge from Jazz Richards inside the box after 73 minutes.
Referee Kevin Friend pointed to the spot, and Baines slotted home into the bottom corner with Tremmel diving the wrong way.
And that was the end of the action as the Swans exited the competition at the fifth stage, with Monk's side now focusing on their Premier League and Europa League commitments.