Ajax make it a hat-trick thanks to Andrews treble
In a goalless first half, Lewis Fathers came closest for the home side when his shot from close range was well saved by the Coventrians goalkeeper.
At the other end, Coventrians winger Lewis Chester failed to hit the target when well placed on the left-hand side of the box.
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Hide AdThe away side started brightly in the second half with goalkeeper Richard Layton making two good saves inside the opening ten minutes.
However, it was Ajax who finally broke the deadlock in the 67th minute when Alex Andrews was put through on goal and his left-foot strike looped into the net.
Two minutes later, Andrews doubled the lead after a flowing one-touch move involving debutant Jack Banks, Matt Layton and Fathers, sidefooting home after the latter had audaciously scooped the ball over the heads of the Coventrians centre-backs.
Andrews then claimed his hat-trick when he picked up a Banks through ball before rounding the goalkeeper and calmly slotting home to make it 3-0.
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Hide AdCoventrians pulled a goal back in the 88th minute when a left-wing cross was not dealt with and Nathan McGarrity prodded home from close range.
Ajax make the short trip to Leamington Hibernian on Saturday.
Hibs beat Shipston Excelsior 2-1 on Saturday to record their first win of the campaign.