Attinella was forced to make another great save minutes later when Dwyer teed up Seth Sinovic to strike from the edge of the area, but the keeper tipped his powerful shot over the bar.
The visitors were having to endure a lot of pressure and Attinella was forced into action yet again, this time to stop Benny Feilhaber's volleyed effort from finding the bottom corner.
After the break, Sporting kept up their assault on the Real goal and Graham Zusi should have given them the lead as he raided into the box, but from close range he put his left-footed shot wide.
The home team came their closest to finding the net when Dwyer beat the offside trap and rounded Attinella, but from a tight angle his shot hit the post and was cleared by the Salt Lake defence.
Kansas City's frustrating match got worse when Oriol Rosell was given a straight red card for a late challenge on Devon Sandoval, reducing them to 10 men for the last seven minutes.
However, Salt Lake couldn't make their advantage count and the match ended in a draw.