The new manager's first win, a 2-1 triumph in Montenegro, was built on a flying start in which Wales had scored both their goals in the opening three minutes.
They had to wait a little longer here but were still 2-0 up inside half an hour.
Whereas torrential rain and gusting winds caused chaos in Montenegro, the sub-zero Icelandic temperatures were more conducive to Wales’ fluent new playing style, albeit another challenge for their travelling fans.
More than a fifth of the 5,200 or so spectators at the picturesque Laugardalsvollur Stadium had come from Wales, swapping their customary bucket hats for woolly ones in the chilly Nordic air.
Their loud presence gave Johnson's opener the feel of a goal for the home side.
The Tottenham Hotspur forward reacted quickly to tap in from close range after Iceland goalkeeper Hakon Valdimarsson had saved Wilson’s initial effort and then attempted to nudge the ball away as it trickled towards the net.
Iceland clearly did not learn from that goal – which had originated from Williams' fine ball over the top for Wilson – because they conceded another in the same manner 18 minutes later.
This time the left-back was further out as he lifted a pinpoint diagonal pass deep from his own half and over the Icelandic defence to Wilson, who brought the ball down elegantly and fired confidently past Valdimarsson.
Wilson had another shot deflected against the post in between those goals, while Sorba Thomas had a shot saved by Valdimarsson, but Iceland carried a threat too.
Andri Gudjohnsen, son of former Chelsea striker Eidur, was denied by a brilliant goal-line block by Williams, and the hosts wasted a hatful of chances early in the second half.
Image source, FAW
