Now Ukraine moves on to face Wales on Sunday with a place in the World Cup at stake.
The winner in Cardiff will go to Qatar in November to play in a group against England, the United States and Iran.
Ukraine put in a slick display despite using six starters who had not played a competitive game of any kind since December.
Most of Ukraine's squad play for home-based clubs whose league was shut down after Russia's invasion, and the playoff in Glasgow was postponed in March. FIFA and Scotland agreed to give the Ukrainian team a fair chance to prepare for games that have become a focus of national identity and pride.
Scotland lacked the class needed and its wait for World Cup soccer now extends beyond the 24 years since it went to the 1998 tournament.
Ukraine's win could have been sealed earlier but for saves early and often by 39-year-old Scotland goalkeeper Craig Gordon. When the Scots chased a way back into the game, John McGinn placed a 67th-minute header inexplicably wide from close range.
Ukraine is riding a wave of global goodwill as the victim of Russian aggression and its players' intense motivation to reward the nation with a place on soccer's biggest stage was clear.
The Ukrainian players all walked onto the field with a blue and yellow national flag draped on their shoulders.
The warm welcome saw Ukraine's national anthem "Shche ne vmerla Ukrainas" applauded loudly by Scotland fans.
Among the crowd of 51,000 were at least 3,000 Ukraine fans, some who traveled far and had made plans to stay in Britain for the decisive playoff Sunday.
George Butromeyev told The Associated Press before the game he came from Toronto with friends to support the players who "need to show the people of Ukraine that we are warriors."
