Michael Laudrup's men enjoyed the majority of possession in south Wales but could not break down the Hammers, who enjoyed chances of their own on the counterattack.
Sam Allardyce's side, looking for back-to-back away wins after a stunning 3-0 success at Tottenham earlier this month, caused the home defense problems with set pieces throughout, though the team was guilty of wasting a number of chances in the first half.
|VIEW FROM THE LIBERTY STADIUM
|By Tom Davies
It was Swansea’s third game in eight days and it showed as the team was slow out of the blocks against a well-organized side. On another day, the Hammers could have been two goals up by halftime, but unfortunately for them it was right back Guy Demel who spurned the best two chances of the game.
Michel Vorm was close to pushing the ball into his own net but was spared the blushes by Angel Rangel who hooked the ball off the line. Chances fizzled out in the second half but the draw was fair, if not the most entertaining.
Swansea was boosted by the return of captain Ashley Williams, making his first appearance in more than a month after suffering an ankle injury, while West Ham was unchanged from the side that lost 3-1 to Manchester City last week.
West Ham made a lively start to the opening exchanges and Stewart Downing's low drive forced Swansea goalkeeper Michel Vorm into a save at his near post after he cut in from the right.
The home side had a great chance to open the scoring on 16 minutes, but Chico Flores' header was powered straight at Jaaskelainen from Jonathan de Guzman's corner.
West Ham broke immediately following Chico's close call and Ravel Morrison went close, dragging an effort wide from the left after Ricardo Vaz Te had played him in.
The chance boosted the visiting side, which then enjoyed a repeated spell of corners, with Guy Demel going closest when unmarked, though he conspired to head over from close range.
West Ham was dealt a blow in the 34th minute when Vaz Te left the field with a wrist injury, to be replaced by Matt Jarvis, but finished the first half strongly in a display that would have given Allardyce confidence.
Swansea looked to press higher up in the pitch in the second half, however, and Spanish forward Alvaro Vazquez was agonizingly close to getting on the end of a Nathan Dyer cross.
Laudrup replaced Vazquez with Wilfried Bony and he almost made an immediate impact, forcing Jaaskelainen into a superb reflex save from six yards.
Swansea enjoyed an extended spell of pressure in the final 15 minutes of the game, and had claims for a penalty after Nathan Dyer's cross struck Joe Cole, but the protests were denied as both sides settled for a point, though it means Swansea has failed to win back-to-back Premier League games in 2013.