Mads Andersen put the visitors in front after four minutes then Conor Chaplin doubled the lead midway through the second half.
Gerhard Struber used two different teams in each half, both in the 3-4-1-2 formation while his side were always on top against the newly-promoted Alex who had not played in almost six months after the League Two season was cancelled in March.
The Reds began well and took the lead in the fourth minute, with Mads Andersen volleying in a right-wing Callum Styles corner at the near post.
Styles then took another corner from the other side and Jacob Brown volleyed just wide from a difficult position at the back post.
Patrick Schmidt should have made it 2-0 midway through the first half when he latched onto a pass by Alex Mowatt and was through one-on-one but smashed his powerful low shot off the base of the left post.
Crewe's only chance of the first half came when Jordan Williams lost the ball in his half and Luke Thomas had to make a last-ditch challenge in his box, then he needed treatment on his calf but completed the rest of the half.
Struber sprang a surprise in the second half by playing young strikers Victor Adeboyejo and George Miller as left and right wing-back respectively. They both had shots from outside the box before the hour-mark with Miller's effort deflected well wide then Adeboyejo's powerful effort was straight at the goalkeeper.
The second goal came on 71 minutes when Conor Chaplin netted a fine header from a left-wing cross by Clarke Oduor.
New signing Dominik Frieser played in Elliot Simoes on the left of the box but the powerful shot was straight at the goalkeeper who palmed it clear. Crewe had their first shot on target seconds later but Brad Collins pushed the powerful 20-yard strike away.
FIRST HALF (3-4-1-2):Walton; Sollbauer, Andersen, J Williams; Ludewig, Mowatt, Thomas, Styles; Woodrow; Brown, Schmidt
SECOND HALF:(3-4-1-2): Collins; Moon, Halme, Oduor; Miller, Wolfe, Ritzmaier, Adeboyejo; Simoes; Frieser, Chaplin
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