The young striker took his tally for the season to seven and Tom Pope sealed the win with a thumping header after Joel Porter had reduced the arrears for Hartlepool.
But the north-easterners were deservedly beaten by a Crewe side that coped better with the windy conditions and poor playing surface.
Hartlepool had few efforts on goal. One threat in the first half saw Anthony Sweeney drive a shot past the post but Crewe came close in the 19th minute when Julien Baudet connected with a Kenny Lunt corner and thudded a header inches wide of the near post.
Maynard then made the most of George Abbey's long low cross from the right wing a minute later. The striker went for the ball with Pools' left-back Richie Humphreys, got the decisive touch and diverted it home.
Then, when Pope headed another Abbey cross onto the post, Maynard was in quickly to finish off ten minutes later.
Michael O'Connor and Maynard again had chances to add to the score before Crewe were lucky to survive a penalty appeal when Patrick Boyle barged Porter off the ball inside the box.
Godwin Antwi made a decisive sliding tackle to deny Maynard his hat-trick at the start of the second half and, while Hartlepool came more into the game in terms of possession, they created little.
Andy Monkhouse's long-range effort was scrambled away from the bottom corner by Crewe keeper Ben Williams, but it wasn't until nine minutes from time that Porter broke onto Gary Liddle's throughball.
Danny Woodards failed to clear the danger and the Pools striker was left to run in on goal and finished clinically.
Just as Crewe fans were fearing a tense finish, Pope rose unchallenged in the 85th minute to head home Lunt's cross and seal an important victory for his relegation-threatened side.