Confusion in the Unirea area saw a half-clearance dribble to the Argentine midfielder 25 yards out and a powerful strike flew into the back of the net.
Iceland midfielder Sigurdsson was unfortunate eight minutes into the second half when his free-kick from 30 yards out came back off the post with Jamie Ashdown beaten.
Everton finally hit back in injury-time as striker Louis Saha, who replaced midfielder Leon Osman in the second half, netted after Steven Pienaar's shot was blocked.