Scotland s Scott Midfielder McTominay reacts, during the Euro 2024 Group A qualifying soccer match between Scotland and Cyprus at Hampden Park, in Glasgow, Scotland, Saturday March 25, 2023. Courtesy of UEFA EURO 2024 twitter account
Aston Villa midfielder John McGinn put Scotland ahead in the 21st minute but from then it was a largely drab contest until Manchester United midfielder Tominay came off the bench to score in the 87th minute before adding another goal from close range in stoppage time.
Cyprus ended the match with 10 men after Nicholas Ioannou was sent off for a second bookable offence, having booted the ball away.
Scotland's victory in Glasgow marks the first time they have won their opening European Championship qualifier since 2006.
But a sterner test awaits on Tuesday with the visit of Spain.
Nevertheless, this was a morale-boosting success, with Saturday's win coming just two days after it was announced Scotland manager Steve Clarke had agreed a new deal to stay in charge of the national side until the 2026 World Cup.
Scotland goalkeeper Angus Gunn, handed his debut in place of the injured Craig Gordon, was first involved in the 17th minute when he made a comfortable save following a long-range shot by Grigoris Kastanos.
Minutes later a dull match sparked into life when Scotland went ahead.
Scotland captain Andy Robertson's deflected cross found McGinn, who volleyed in from close range at the back post, although it need a lengthy VAR check to confirm the goal.
The match, however, then reverted to type and the mood became increasingly tense late on when Gunn, the son of former Scotland No 1 Bryan Gunn, saved well from Andronikos Kakoullis's deflected drive.
But the home crowd's nerves were eased when McTominay struck from three yards after Lyndon Dykes headed down a cross from Ryan Christie, with the United midfielder on target again from 12 yards in the third of five added minutes.
And there was still time for Ioannou's act of petulance to be punished by a red card.
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