The 20-year-old striker suffered a broken leg in a challenge with Brighton's Kerry Mayo midway through the first half.
Maynard, who was Crewe's second leading scorer last season, is likely to be out for several months.
The Railwaymen had already turned to youth when they included 18-year-old Byron Moore in the side after Ryan Lowe was ruled out with an ankle injury.
Moore was sent to play in attack alongside another teenager Shaun Miller after Maynard was stretchered off and Crewe struggled to offer a threat on goal.
They were indebted for the three points to midfielder Gary Roberts, who netted twice. After Dean Hammond was adjudged to have handled Billy Jones' cross, Roberts fired the spot-kick past Michels Kuipers to cancel out Dean Cox's opener.
Cox brought down Mayo's delivery with some skill before firing across Ben Williams into the bottom corner to hand the visitors a deserved lead.
They had already struck the woodwork when Hammond connected with Andrew Whing's cross with a powerful looping header.
Crewe struggled to make inroads for much of the afternoon and Brighton were dangerous again after the break with Tommy Fraser flicking a header onto the bar.
But Crewe got the breakthrough 11 minutes from time when Jones curled in a telling cross to the far post and Roberts arrived to head home.
Albion's woe was complete when Dean Cox was tripped by Moore inside the box in the closing minutes, but the referee awarded a free-kick a yard outside the box.