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Quickfire goals at the end of the first half from Jason Cowley and Milan Butterfield put the Yeltz in command at the break.
And Vanylson Silva netted a second-half brace to take the tie out of Evesham’s reach as Mike Ford’s suffered a sixth successive defeat in all competitions.
The Yeltz made a bright start as Samson Hewett’s attempted cross hit the post with the former trying to pick out Cowley in the box.
And Butterfield then fired narrowly over the crossbar from 30-yards out while Todd Parker shot wide as the visitors remained on top.
Evesham tested the Halesowen goal for the first time just before the half-hour mark as Aaron Heap drove through midfield but could only shoot straight at Yeltz goalkeeper Dan Platt.
And the Robins went close again later in the first half as Ryan Wynter glanced Kai Churchley’s corner into the centre of the box before Silva blocked a follow-up effort on the line.
However, Halesowen broke the deadlock three minutes before half time when Hewett’s corner fell kindly to Cowley in the box who finished at the near post.
And the Yeltz struck again moments later as Butterfield beat Brendan Beard in the Evesham net with a long range strike into the bottom right corner.
The visitors extended their lead on 53 minutes when Silva rose highest to head Cassidy’s cross into the net and put the tie beyond doubt.
And Halesowen scored a fourth goal just past the hour mark when Silva poked home at the second attempt from another Cassidy cross after Beard made an initial save.
Silva almost completed his hat-trick late on only for Beard to make a save with his legs with United unable to find a consolation goal in the remaining minutes.
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