The Swans secured another hard-fought point at Everton to take their unbeaten run to seven games in all competitions.
Michael Laudrup's side had to put in a stern defensive performance against an Everton side that they had never beaten in any competition and had lost their previous three Premier League encounters to.
But it was a point they battled hard for, with Ashley Williams and Chico Flores standing tall against the likes of Marouane Fellaini, Nikica Jelavic and Victor Anichebe, who all went close while Dwight Tiendalli and Williams both cleared off the line.
Michu went the closest for the Swans as the Spaniard's delightful lob almost catching Tim Howard out, but the American tipped the effort onto the crossbar in the first half.
This result moved the Swans onto 30 points from 22 games, with Laudrup's men remaining in ninth place.
Laudrup made four changes to the starting XI that beat Chelsea in the Capital One Cup in midweek.
Michel Vorm was restored in goal despite Gerhard Tremmel's heroics at Stamford Bridge, while Dwight Tiendalli returned to right-back as Angel Rangel moved to right-wing - a position where he finished the cup win in London.
Also back in the XI were Kemy Agustien and Nathan Dyer - who started up front - as the Swans looked to claim their first win over Everton in any competition.
Everton: Tim Howard, Leighton Baines, Phil Jagielka, Nikica Jelavic, Sylvain Distin, Phil Neville (capt, Steven Naismith, 69), Leon Osman, Steven Pienaar, Seamus Coleman, Marouane Fellaini, Victor Anichebe (Apostolos Vellios, 84).
Subs: Jan Mucha, Bryan Oviedo, Thomas Hitzlsperger, Matthew Kennedy, Shane Duffy.
Swans: Michel Vorm, Dwight Tiendalli, Chico Flores, Ashley Williams (capt), Ben Davies, Kemy Agustien, Ki Sung-Yueng, Michu (Danny Graham, 82), Angel Rangel, Pablo Hernandez (Wayne Routledge, 73), Nathan Dyer (Jonathan de Guzman, 58).
Subs: Gerhard Tremmel, Kyle Bartley, Garry Monk, Leon Britton.
Everton made a bright start, and Michel Vorm had to be alert in the second minute as he raced out to firstly deny Nikica Jelavic before getting to the loose ahead of Victor Anichebe after Ben Davies' weak back pass.
Davies then did enough to put Jelavic off as the Croatian side-volleyed Steven Pienaar's just wide, and the striker was at it again shortly after as he saw his header from Leighton Baines' corner hacked clear by Dwight Tiendalli.
From the resulting clearance, Pablo Hernandez raced past Phil Neville and into the Everton half and when he spotted Nathan Dyer free on the right, he threaded through a pass only for Tim Howard to intercept.
Everton responded via Anichebe, who got onto the end of Marouane Fellaini's knockdown but Michel Vorm took the sting out of the effort before Ashley Williams got rid of the loose.
Then the Swans went the closest to breaking the deadlock. Dyer slipped through to the onrushing Michu, and the Spaniard's attempt to to chip Howard was tipped onto the crossbar and out for a corner by the American.
Leon Osman, who scored the only goal in this fixture last season, then nodded wide from a free-kick when well placed as the game went into the break scoreless.
Half-time: Everton 0 Swans 0
Everton were quick out of the blocks again after the restart and Vorm did well to parry Seamus Coleman's effort within the first minute.
Hernandez then worked himself into space but his left-footed shot was easily gathered by Howard as the Swans offered a response.
Laudrup then made a change just before the hour as Jonathan de Guzman replaced Dyer, with Michu moved up front and the Dutchman slotted in as the attacking member of the midfield.
Both sides seem to cancel each other out for the next ten minutes, and as a result both managers made substitutions.
David Moyes brought Steven Naismith on for Phil Neville while Laudrup introduced Wayne Routledge in a straight swap for Hernandez.
The home crowd were on their feet in the 75th minute as Baines' corner dropped to Phil Jagielka, but the England centre-back's header rose over the crossbar from eight yards.
Laudrup made a final change for the last eight minutes, Danny Graham coming on in place of Michu.
It made for a tense finish, and Jelavic wasted a decent chance when he fired over from ten yards with seconds left of normal time.
The Swans had to dig deep, and they got a point - and a clean sheet - for their efforts.