The Toffees' fine start to the season continues as they pick up a comfortable win at the Liberty Stadium thanks to a powerful performance from the Belgium international
The Toffees dominated the first period and enjoyed a two-goal half-time lead courtesy of strikes from Victor Anichebe and Kevin Mirallas.
Nathan Dyer, introduced as a half-time substitute, was sent off early in the second period to all-but end the home side's chances of victory and Marouane Fellaini's header sealed the win for the Toffees.
Michael Laudrup made two changes to his side, giving full Premier League debuts to Ki Sung-Yueng and Pablo Hernandez, while the Toffees made three alterations, with Victor Anichebe replacing the injured Nikica Jelavic. Seamus Coleman and John Heitinga came in for Tony Hibbert and Sylvain Distin.
Everton started the game in dominant fashion with Anichebe and twice Mirallas drawing smart stops out of Michel Vorm in the opening five minutes.
The Merseysiders' pressure was relentless and they grabbed a deserved lead in the 22nd minute. Leighton Baines' free kick into the box was chested down by Fellaini, and the Belgian seemed to use his arm, under pressure from Alan Tate, to nudge the ball to Anichebe, who smashed home from six yards.
The game passed the half-hour mark and Swansea finally managed to put an attack together. Jonathan de Guzman looked to thread a pass to Michu, who returned the ball to the Dutchman with Howard racing off his line, De Guzman attempted to chip home but Phil Jagielka recovered to head off the line.
The Spanish playmaker then went close himself, narrowly heading over from Hernandez's corner before Ki curled a magnificent effort just past the post as the Swans fully awoke from their earlier slumber.
With the home side pushing forward, they were caught on the break, Fellaini released Steven Pienaar down the right and the South African's first-time centre found Mirallas who headed his first Premier League goal home after Vorm had stopped his initial effort.
The Swans should have grabbed a goal back at the end of the half but Angel Rangel saw a weak one-on-one effort saved by Tim Howard before inexplicably skewing an effort away from goal, after getting on the end of Wayne Routledge's dipping cross.
The Swans introduced Dyer for the second half in place of Hernandez, as they searched for a way back into the match.
The game continued at a frenetic pace after the restart, Mirallas rattled the bar with Vorm called into action by Anichebe on the rebound before Ki burst forward, drawing a low save out of Howard.
Laudrup felt the need to make another change, bringing on Leon Britton for Tate, with the South Korea international dropping into the defence.
However, things went from bad to worse as Dyer, having already been booked for dissent, clattered Baines and picked up a second yellow card to be sent off just 12 minutes after being introduced.
The Toffees were controlling the game comfortably against 10 men and should have extended their lead further as Baines released Anichebe in the left channel but Fellaini skied his effort from the Nigerian's cut back.
The Belgian went close again, heading Osman's corner goal-wards but Britton managed to scramble the ball away from his position on the far post.
As the game entered its final 10 minutes, Fellaini finally had his goal. Baines' free kick was perfectly measured onto the towering midfielder's head and his effort ended up in the back of the net via a deflection off Ashley Williams' shoulder.
The Toffees saw out the game comfortably, also introducing Bryan Oviedo late on for his Premier League debut as they preserved their long-running unbeaten run against the Swans.