And Toshack's tots - with an average age of 22 - enjoyed plenty of early possession but Iceland should have punished the Welsh for not penetrating in their early dominance.
Palmi Palmason broke free in the box but his low shot was blocked thanks to Craig Morgan's timely last-ditch challenge.
The Valur attacker, though, should have given Iceland the lead in the 12th minute but the fact he did not was down to Wayne Hennessey's top-class reflex save.
Palmason dashed onto Bjarnason measured chip over the flat-footed Wales defence but his left-foot volley from eight yards was superbly saved at point-blank range by Wales keeper Hennessey.
The Welsh - minus eight key players including Gareth Bale, Simon Davies and Danny Gabbidon - weathered Iceland's storm in the land of the midnight sun and Toshack's young side regained a foothold in this friendly.
Jack Collison and Carl Fletcher looked to make the most of Wales' territorial advantage but their long-range efforts didn't find their intended target.
Fletcher's night of supposed joy ended in misery for the stand-in skipper as his big day ended abruptly in the 37th minute when he has hacked to the ground by Palmason.
The Crystal Palace midfielder was stretchered off with suspected ankle ligament damage and was replaced by rookie Evans - and the 19-year-old striker made a stunning impact.
Joe Ledley burst down the left wing and whipped the ball dangerously low across the six-yard box and Evans finished with cheeky brilliance.
His audacious Kanu-esque back-heel surprised everyone including Iceland keeper Kjartan Sturluson who was left rooted to the spot as the flick crept into the far post.
Sam Vokes' arrival for Freddy Eastwood just after the break amazingly made the Wolves new signing the 32nd new cap in Toshack's 32-game reign as Wales boss.
But it was that man Evans that almost laid on a second for Wales as the young tyro set up second-half skipper Jason Koumas, whose 25-yard volley fizzed inches over Sturluson's crossbar.
Star striker Craig Bellamy gave Toshack and Wales fans more reasons to cheer on the hour as the West Ham hero ended a season of torment - a hip injury kept him out for virtually seven months - with half-an-hour remaining in the Laugardalsvollur Stadium.
And a typical Bellamy burst down the right flank almost teed up a second Wales goal in the 28-year-old's 50th Wales international.
His wicked cross from the byeline caused chaos in the Iceland six-yard box and Vokes was just a whisker away from emulating Evans and scoring on his senior Wales bow.
The visitors had to withstand relentless late pressure from the hosts and Palmason missed another great opening but the winger sliced his chance wide.
Wales' wonder kids late on showed they have resilience and brass in equal measure to stand firm and hold on.
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