Watford boss Ray Lewington celebrated what he described as an "essential victory" but warned there are still some "twists and turns to come before the end of the season".
The Hornets moved three points further away from the relegation zone with most of their rivals' results going their way.
"We are now a point behind Crewe so we have brought them back into the equation," said Lewington.
"But if we lose on Monday and the others win it will be back to the same situation. I've always said we need 50 points but it may well take more than 50 to get clear." Watford were good value for their win although they were hanging on at the end.
Admitted Crewe boss Dario Gradi: "I still thought we might equalise right up to the last free-kick but we did not look dangerous and Watford got through our midfield too easily." Not surprisingly it wasn't a classic. The first half-hour saw Watford look the more dangerous but their final ball lacked penetration.
Crewe keeper Ben Williams had to dive to his right to tip away a fierce drive from Gavin Mahon but otherwise it was a tepid start.
Even so, Watford looked the most likely and duly provided a goal on the half-hour.
Micah Hyde produced his first goal in over a year firing home at the second attempt from just inside the box after being set up by Heidar Helguson.
Helguson and Lee Cook went close as Watford looked to increase their lead but they had a scare just before the interval when Steve Jones broke clear on the left but the Crewe substitute sent his drive beyond the far post.
Crewe broke back on the hour. They had just produced their first on-target attempts of the game but, when Jones was heading out of the penalty area, Watford's Cook felled him with a clumsy challenge to provide Dean Ashton with a chance to level the scores from the spot.
Watford duly replied within 90 seconds. Mahon broke through the middle to set up Cook for a shot. Stephen Foster attempted a clearance which hit David Wright and bounced into the Crewe net for what proved to be the winning goal.