Tom Butler's early strike set leaders Swansea on their way with the early opener, before Paul Anderson's stunning solo strike sealed the points as they edged closer to the Championship.
Crewe striker Tom Pope grabbed an injury time consolation, but it counted for nothing as Crewe continue their battle to avoid relegation.
Swansea made three changes to the side which beat Port Vale last weekend with Dennis Lawrence, Andy Robinson and Guillem Bauza all included.
Crewe coach Steve Holland was forced into major surgery on his side with five new faces, including on-loan Everton defender Pat Boyle making his debut.
Swansea began on top and Robinson and Ferrie Bodde saw early shots drift wide.
But it was no surprise to see the Welsh side take the lead and it was Butler who had time and space to rifle home the 14th minute opener.
Bodde screwed a mis-hit a shot into the winger's path and Butler made no mistake with his low shot past Crewe goalkeeper Ben Williams.
Crewe's Nicky Maynard saw a spectacular scissor kick bounce agonisingly wide in a rare foray forward into Swansea's half.
But the Welsh side were well on top and Bauza and Darren Pratley come close to extending their lead as the Railwaymen somehow hung onto their one-goal deficit at the break.
Williams' heroics continued to frustrate the Swans as Robinson and Lawrence became the latest players to be denied as Roberto Martinez's side looked for the breathing space.
It seemed only a matter of time before Swansea extended their advantage and it arrived when Anderson wrapped up the points, before Pope set up the grandstand finish.