The Swans shared the spoils with Manchester City in an even contest at the Liberty Stadium.
The first half was the far livelier of the contest, with Pablo Hernandez, Michu and Wayne Routledge going close while the Swans had a very strong case for a penalty after Matija Nastasic clattered Michu in the box, but the appeals were turned down.
Ashley Williams and then Michel Vorm denied David Silva from close range before the break, while in the second half sub Edin Dzeko missed a glorious chance from six yards out.
This point moved Michael Laudrup's side onto 43 points with three games remaining as they continue their target of a top-half finish.
The Swans made one enforced change to the starting XI. Ki Sung-Yueng missed out due to a thigh problem, with Michael Laudrup handing Nathan Dyer - who came off the bench the previous week at Chelsea - a start.
Swans: Michel Vorm, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton, Jonathan de Guzman, Wayne Routledge (Kemy Agustien, 64) , Nathan Dyer (Dwight Tiendalli, 86), Pablo Hernandez, Michu (Luke Moore, 70).
Subs: Gerhard Tremmel, Garry Monk, Neil Taylor, Itay Shechter.
Manchester City: Joe Hart, Pablo Zabaleta, Vincent Kompany (c), Gael Clichy, Matija Nastasic, Yaya Toure (Edin Dzeko, ht), James Milner, Samir Nasri, Gareth Barry, David Silva (Jack Rodwell, 85), Sergio Aguero (Carlos Tevez, 79).
Subs: Costel Pantilimon, Kolo Toure, Aleksander Kolarov, Javier Garcia.
Prior to kick-off, the club marked the ten-year anniversary of retaining their Football League status with former boss Brian Flynn given a standing ovation on the pitch.
Both sides settled into the encounter early, with the Swans creating the best chance of the opening 20 minutes.
Angel Rangel threaded through a pass for Nathan Dyer, and his cutback teed up Pablo Hernandez but the Spaniard's effort was high and wide.
Then came two more big chances. Wayne Routledge collected a return pass from Michu inside the box, but when he was about to shoot, Samir Nasri poked the ball out for a corner.
Just 60 seconds later the home fans were on their feet again, Dyer finding Michu with a superb cross, but the Swans top scorer volleyed just wide of the far corner.
The Swans probed again, Hernandez's sublime crossfield pass finding Dyer, who raced on before cutting back to Routledge, but his shot on the turn in side the box was comfortably dealt with by Joe Hart.
Hernandez was causing the visitors defence problems, and when he raced onto Routledge's through ball, the Spanish international was forced inside before screwing his shot the wrong side of the post.
Manchester City responded via Samir Nasir, who flicked on Gareth Barry's chip into the box but Michel Vorm reacted well to gather.
The Swans then had a very strong penalty appeal turned down as Matija Nastasic clattered into Michu inside the box as the Spaniard beat him to the ball, but referee Mike Jones waved play on.
City then sprang into action as David Silva turned Chico and as he unleashed from ten yards, Ashley Williams timed his block perfectly. Then, from the loose, Vorm was quick to react and deny Silva with a fine block.
Half-time: Swans 0 Man City 0
Roberto Mancini made a change at the break, Edin Dzeko replacing Yaya Toure.
Both sides cancelled each other out for the the start of the half, prompting Michael Laudrup to make his first change just past the hour as Kemy Agustien came on for Routledge.
Another change followed, Luke Moore replacing Michu up front.
Neither team were creating too many problems for each other, Jonathan de Guzman's free-kick that failed to threaten Hart was the only action of note.
Mancini made another substitution for the final ten minutes as Carlos Tevez replaced Sergio Aguero.
The visitors then had two golden opportunities to break the deadlock.
First, Dzeko missed the target from six yards after Pablo Zabaleta's cross fell to the Bosnian after deflecting off Hernandez, and then Silva's thunderous effort from 12 yards whistled past the post.
Dzeko then tested Vorm with a glancing header in added on time, with both sides having to be content with a share of the spoils.