Sigurdsson, who plays in the English Premier League with Swansea, grabbed his first from the penalty spot after Stefan de Vrij fouled Birkir Bjarnason, firing powerfully past Jasper Cillessen.
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.