The PSV Eindhoven captain started at right wing-back for the Dutch, and he produced a sublime attacking display over 90 minutes.
The 25-year-old was guilty of squandering two clear-cut scoring chances in the first half but made amends following the interval.
He played his part in the goals scored by Georginio Wijnaldum and Wout Weghorst before the hour mark of the encounter.
Ukraine made a terrific comeback with two quick-fire goals in the 75th and 79th minute, but the Dutch still prevailed with a win.
Dumfries found the winning goal with a header five minutes from time after a delightful cross from Nathan Ake from the left flank.
The Toffees are leading the race to sign Dumfries this summer, but his display last night would have caught the eye of top European clubs.
Some of the Toffees fans were hopeful that the club have an agreement in place to sign him, while others urged them to seal a quick transfer.
Here are a few reactions on Twitter.
— Rob Vera (@TheRobVera) June 13, 2021
I hope weve agreed a fee on dumfries already #EFC
— Ryan O'Hanlon (@RyanOHanlon1) June 13, 2021
Cracking game that. Been a decent tournament so far. Got to hope that a deal for Dumfries was done before tonight!
— Paul EFC 86 (@PaulEFC86) June 13, 2021
Sign him up quick #dumfries
— Nick Gartland (@nickgartland) June 13, 2021
Sign Dumfries up tomorrow @Everton talented kid him.
— Ste P. ⚽️ UTFT. (@PapaSmurf1878) June 13, 2021
Dumfries looks class.
— Bradielka (@EvertonEFC18788) June 13, 2021
Dumfries has played at right-back during his time at PSV. Last season, he registered four goals and nine assists from 41 appearances.
He featured in an unfamiliar right wing-back role yesterday and produced a superb showing as he largely operated in the opposition half.
He did not have to do much defending but still won more aerial duels (4) than anyone.
Dumfries can’t be judged on one performance, but it has got some Toffees fans talking about the prospect of landing his signature.
The Toffees have Seamus Coleman and Mason Holgate as the right-back options, but the former is no longer in the prime of his career.
Holgate is primarily a centre-back by trade. Dumfries could be an ideal player to complement left-back Lucas Digne next season.
Stats from Transfermarkt.com