Lincoln, who finished the minor-league season at Class AAA Indianapolis, was the winning pitcher in relief. He allowed three runs and six hits in 4 1/3 innings with one walk and two strikeouts.
Alvarez, who finished the season at Class AA Altoona, went 0-for-4 with a two strikeouts.
"We were excited about them getting the opportunity to go out there, compete at the international level and extend their seasons by a month," Pirates general manager Neal Huntington said. "They've done a great job. To represent your country is a tremendous honor and a great opportunity for these guys to get to do in their development."
Lincoln was 3-0 with a 2.70 ERA in four games, three starts, during the tournament.
He really did a heck of a job," Huntington said. "He started. He threw strikes. He threw well in big games for them. It was a great experience to extend his season by a month and compete internationally."
Alvarez hit .259 with five home runs and 12 RBIs in 15 games.
"Pedro has swung the bat well and with power," Huntington said. "Also, our reports coming back were that he's played great defense."
Lincoln, 24, went a combined 7-7 with a 3.37 ERA in 25 stars with Indianapolis and Altoona this year. Alvarez, 22, was the Pirates' minor league player of the year after hitting a combined .288 with 27 home runs and 95RBIs in 126 games with Altoona and high Class A Lynchburg.
Huntington indicated both Lincoln and Alvarez will be given chances to win a spot on the major-league club next year in spring training along with outfielder Jose Tabata,who ended the season at Indianapolis. Tabata, 21, hit a combined .293 with five homers, 35 RBIs and 11 stolen bases with Indianapolis and Altoona in 93 games.
"They'll all get a look but they'll also have their work cut out for them next spring," Huntington said. "They'll need to come in and show improvement if they are going to make the team."