Saudi Arabia's defence was in shambles early on and they didn't look much better at the other end with their only attacking chances coming from counter attacks - none of which forced a meaningful save from New Zealand goalie Glen Moss. He wasn't needed until the 56th minute and wasn't tested again for another 20 minutes after that.
Midfielder Chris James made the most of a rare start with a solid outing and almost put the All Whites in front with a free kick in the 75th minute, with his shot curling over the wall and just over the top right corner of the goal.
Just three minutes later however Killen scored the winner after receiving the ball on the edge of the box from Barbarouses, he dipped a shot into the lower right hand side of the goal.
All Whites captain Winston Reid said it was a good win in the circumstances.
"When people are tired they had to put their hands up and we made substitutions at the right moment," Reid told RadioSport.
"And in general I thought it was a good performance away from home and in some tough conditions.''
In the earlier match UAE, ranked 84th in the world, defeated Trinidad and Tobago on penalties after it ended in a 3-3 draw.