Stankovic came out of retirement to captain his country, playing the first 11 minutes in Novi Sad before being withdrawn.
The appearance moved the 35-year-old to 103 caps, with Serbia going on to win 2-0 courtesy of second-half goals from Dusan Tadic and Milos Jojic.
The former Inter midfielder - who announced his retirement at the end of the season following nine years at San Siro - said he was grateful to lead his country out on his final appearance for the national team.
"Every game I played (has been) sublimed by these wonderful last 10 minutes and I can only thank everyone who turned up to make it a memorable afternoon," Stankovic told Serbian television.
"There were ups and downs, trials and tribulations and I am just grateful I could put on the captain's armband one last time."
Serbia coach Sinisa Mihajlovic, a team-mate of Stankovic at Inter and Lazio, paid tribute to the midfielder's commitment.
"Stankovic gave his entire self to the national team and I am delighted that he has become our most capped player," he said.
