The Hornets weren’t at their fluent best, but scraped a victory to make it seven games unbeaten in Northern League Division Two.
Hebburn started the game with the bonus of Alan Pegram being available and he captained the team.
On a difficult pitch, Crook started brighter, but never troubled Steve Hubery in Hebburn’s goal.
After 20 minutes, Glen Hargrave should have scored from a Lee McMahon corner, heading into the keeper’s arms from five yards, and a minute later he also headed wide from the same distance.
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Hebburn lost centre half Kris Summers to injury just before half time and he was replaced by Mick Watson.
The second half started with Hebburn trying hard to find any fluency in their play as the game was very scrapy.
Hebburn were denied a blatant penalty on the hour when Hargrave appeared to be brought down in the box.
After 65 minutes, top scorer Channon North game on for Callum Smith as Hebburn looked to force a victory. Centre half Ross Toward left the pitch for 10 minutes for attention to a cut eye a result of an elbow from a Crook forward but it didn’t halt the visitors’ progress.
Crucially, with 10 minutes to go, a McMahon cross was headed against the base of the post and North put the rebound in from two yards.
Hebburn comfortably saw the game out for their third clean sheet in a row and seventh game unbeaten.
Boss Scott Oliver said: “We didn’t play well at all, but when you keep clean sheets you always have a chance of a win.
“Credit to our back four which was much changed due to injury. Ross Toward and Ian Bickerstaff were our stand out performers.”