Watford picked up their first win on their travels although they had keeper Alec Chamberlain sent off at Crewe.
The veteran custodian was dismissed after 19 minutes when he was adjudged to have handled outside of the box as he rushed to collect the through ball chased after by Steve Jones.
Despite coming under pressure from the Cheshire side Watford held firm and stole the three points when Danny Weber fired in after taking Jamie Hand's pass.
Hornets boss Ray Lewington declared: "It's a ludicrous law which penalises a keeper when he comes out and he is just marginally over the line.
"We rolled our sleeves up and really had a go and the spirit of the players and supporters has been fantastic."It was the fourth time this season that Watford have had a man dismissed and Crewe should have taken the advantage, but in the absence of their boss who has just had heart surgery, the caretaker management team hasn't had a win in four games.
Neil Baker lambasted his side's approach afterwards particularly in the second half when long balls were lumped forward in the general direction of Dean Ashton, Jones and Paul Edwards.
Despite their going with three up front in the second half, Crewe hardly created anything to worry sub keeper Lenny Pidgeley.
Jones had a header deflected wide following a Kenny Lunt corner and Lunt almost caught out the stand-in keeper with a free-kick way out on the touchline which he clawed away from his top corner and over the bar.
But Watford defended in depth and they deserved the only goal of the game when Crewe made a hash of the clearance allowing Hand to tee up Webber for the finish.