Cambridge United's French manager Herve Renard saw his team finally produce some fire in attack only to be denied by one of his countrymen in Swansea's goal keeper Willy Gueret.
He pulled off a series of tremendous second-half saves as Cambridge fought back after falling behind to a Lee Trundle goal in the 22nd minute.
Three times within two minutes he saved or blocked shots from Darren Quinton, Daniel Chillingworth and Abdou Elkholti.
That period of pressure started in the 16th minute and looked sure to produce Cambridge's first goal in three games, but Gueret was not to be beaten diving at the feet of Jermaine Easter in the 76th and 80th minutes.
He was let off the hook in the 25th minute when Daniel Webb slammed his shot against the post from only eight yards out.
Trundle showed how to finish when he got his chance thanks to a defensive mix-up, lifting a superb shot over the keeper from 20 yards.
He threatened to do it again to give Swansea a second goal their play scarcely deserved in the final minute but this time young keeper John Ruddy parried the shot and the ball was scrambled away for corner.