The Magpies winger saw his 10-month absence from the Scotland squad ended last week when Clarke handed him a recall for Nations League fixtures against Ukraine and Republic of Ireland.
Fraser made his first appearance since he started in a 1-0 win in the Faroe Islands last October when he replaced Stuart Armstrong with 15 minutes remaining at Hampden Park on Wednesday night.
The former Bournemouth man wasted little time in making an impact as he showed his prowess from set-pieces with two fine deliveries that were converted by QPR striker and fellow substitute Lyndon Dykes as their side claimed a 3-0 win over Ukraine.
Clarke reflected on his inspired double-change but handed the credit to the duo, rather than focusing on his own decision.
He told Premier Sports: “It’s always nice as a manager when you make a couple of changes and they’re involved in the next two goals.
“That’s good. The players make it good.
“When you get to that stage of the game, you’re looking for fresh legs.”
The result helped Scotland take some revenge for the World Cup play-off defeat inflicted on them by Ukraine earlier this summer.
The win also takes the Tartan Army to the top of Nations League Group B1 and boosts their chances of topping the group with two games to play.
Clarke warned his squad they have ‘a lot of work to do’ because they can celebrate a successful campaign.
“The way they played, the way they executed the way we wanted to play was excellent.
“It took us a long time to get the goal, but when the goal came, it helped them a little bit and they relaxed.
“We managed to get a couple more near the end, so the scoreline looks good but we still have a lot of work to do in the group.”
United star Fraser will hope to have done enough in the win to earn a place in Clarke’s starting lineup for their Hampden Park meeting with Republic of Ireland on Saturday night.
Their group stage fixtures will then be brought to a close with a game against Ukraine in Poland on Tuesday before Fraser returns to Tyneside ahead of Newcastle’s visit to Fulham on Saturday week.