The home side were the first to threaten the net as Gaston Fernandez found space in the final third, but he could only drag his strike wide of the target.
Dairon Asprilla was the next to go close for the Timbers as he raided down the flank and cut inside onto his right foot before drilling his strike over the bar.
In the second half, Nagbe almost unlocked the New England defence when he latched onto a loose ball in the box and blasted an effort at goal, but Shuttleworth beat the ball away.
Shuttleworth kept the scores level in the 74th minute when he made another fine stop to beat away a powerful header from Maximiliano Urruti.
However, the home side finally found their breakthrough when Fanendo Adi latched onto a cross from Jorge Villafana and powered his header past Shuttleworth.
Adi secured the win for his side as he raced on to a low cross into the box from Alvas Powell and diverted the ball into the net with his left foot.