Billy Kee's header enough for Accrington
Billy Kee scored the only goal of the game as Accrington recorded a first Sky Bet League Two win in 11 matches at Crewe.
A mix-up involving Alex goalkeeper Ben Garratt and defender Harry Davis saw the ball squirm over the line from Kee's header.
Crewe pushed for an equaliser but could not find a way through as Stanley moved to within three points of their opponents.
Shay McCarten was Accrington's danger man in the early stages, hitting the side-netting, sending a volley inches over and seeing a free-kick tipped away by Garratt.
Alex Kiwomya had a half-chance for Crewe just before Kee's goal, while George Cooper brought a decent save from Aaron Chapman early in the second half.
The home side spurned two gilt-edged chances to level as substitute Callum Ainley forced Chapman into another fine stop before Cooper slammed the loose ball into the side-netting.