Bristol City defender Christian Ribeiro raced to the by-line before cutting back to debutant Nathan Craig on the six-yard box, but the Everton striker sent his curling shot inches wide.
Craig had another chance moments after the restart picking up on a loose ball to fire left-footed first-time from 25 yards which goalkeeper Ibrahim Sehic turned over the bar.
But it was Evans who finally broke the deadlock just before the hour. Marc Williams headed Craig's long left-sided free-kick across goal and Evans, who appeared to be offside, headed a looping ball into the next from six yards.
Wales were guilty of switching off soon after and Coric wasted a great opportunity to level when he blasted the ball over the bar from close range.
And with 20 minutes to go, Wrexham keeper Chris Maxwell was almost needlessly embarrassed when he hesitated on a clearance under pressure, but made amends.
Wrexham striker Marc Williams could have wrapped up the win late on, but his connection from a looping ball across the box was comfortable for Sehic to save.
But Evans sealed the win in injury time volleying home from the edge of the box with help from a deflection after the Bosnians failed to clear captain Shaun MacDonald's cross.
Wales under-21 coach Brian Flynn:
"I said to them at half-time that we would get chances and I knew that if they fell to Ched he would take them.
"They made it difficult for us, we had a lot of possession but they were hard to break down.
"Once we scored they had to come out and there were more spaces. We had one or two little scares but nothing of any seriousness."
Wales U21: Maxwell, Morris, Neil Taylor, King, Blake, Ribeiro (Wilson, 52), Richards (Chamberlain, 56), Craig (Bodin, 73), Williams, Evans, MacDonald. Subs Not Used: Cornell, Alfei, Thomas, Jake Taylor.
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