The assist came from the right wide as Shea got a cross into fellow native Texan Clint Dempsey. Shea got free for the cross after right back Steve Cherundolo ran down Shea's initial cross which had been blocked. Dempsey made a nice cut back move to create space and scored with his left foot in the 36th minute.
The United States got Jurgen Klinsmann a victory in his fourth try as American coach.
Goalkeeper Tim Howard made several key saves.
"It's huge for all of us. You don't ever want to go a long period of time without winning," Howard said. "We performed well, I think, and we're trying to set a foundation, but ultimately you have to win. That was the focus coming in."
Since Klinsmann replaced Bob Bradley on July 29 after the CONCACAF Gold Cup, the Americans had tied Mexico, and lost to Costa Rica and Belgium.
On a rainy night in south Florida, a frog could be seen on the field. The game was the first of a pair for the U.S. during the international fixture period. The Americans host Ecuador on Tuesday night in Harrison, N.J.
The U.S. used a 4-1-3-2 formation and Howard made up for a few defensive lapses.
"I think it took us a little bit to get into a higher pace," Klinsmann said. "The first 20 minutes were a bit too static. And then we took over, created a lot more chances."
Dempsey put the U.S. ahead with his 23rd international goal. Shea's centering pass got past several players and touched Michael Orozco Fiscal before Dempsey gained control at the top of the penalty area, He moved the ball from his right foot to his left and shot high past goalkeeper Donis Escobar .
"I didn't know if the ball was going to come through, I got a little lucky," Dempsey said. "I took my time. I was going to take it with my right foot but saw it was going to be blocked, so I pulled it back to my left and couldn't have hit it any sweeter."
Dempsey also appeared to score on a header in the 84th minute, but Dempsey was called for a foul.
The Associated Press contributed to this report.