The Swans made five changes from the side beaten by Huddersfield with Andy Oakes making a surprise debut in goal in place of Willy Gueret.
Tom Williams, Darren Way, Leon Britton and Fallon were recalled to the starting line-up as Kenny Jackett's men looked to bounce back from successive defeats.
Crewe showed three changes following their weekend defeat at Yeovil.
Oakes was called upon twice in the opening minutes but it was the Swans who went closest when Fallon headed down, but Andy Robinson scuffed his shot from close range.
The busy Fallon hit the base of the post with a header in the 15th minute but the ball was safely hacked clear.
Crewe's front two were unable to hold the ball up and Swansea held the visitors back in their own half with Robinson finding plenty of space to rifle in shots on target.
The Swans took a deserved lead in the 24th minute when Williams knocked a high ball in to Fallon, who twisted before volleying over Ben Williams and into the net.
Crewe were thrown a lifeline on the half hour when Oakes brought down Nicky Maynard. Gary Roberts smashed the spot-kick into the roof of the net after Oakes had been yellow-carded.
A deep run by David Vaughan opened up the Swansea defence, but Izzy Iriekpen was on hand to clear Luke Varney's flick as it rolled towards the empty net.
The Swans went back into the lead eight minutes after the restart when Fallon headed back across goal and Knight was in the right spot to turn the ball home.
Four minutes later Way thrashed a shot on to the top of the crossbar with Williams beaten.
Knight and Robinson could have sealed it late on, but Billy Jones made a superb block as the little striker let fly and then Williams stretched to push away Robinson's goalbound drive.