Despite being without a competitive win since November 2024, Sweden began confidently and stunned their opponents by taking the lead after only six minutes.
A smart pass across the face of goal from Benjamin Nygren found Viktor Gyokeres in a perfect position inside the six-yard box, and the Arsenal striker made no mistake to net his 16th goal for his country - his first since November 2024 - giving Blagult a dream start.
Potter's side came within inches of doubling their advantage shortly after the midway point of the first half, as Gabriel Gudmundsson’s effort glanced off the post following a superb, surging run through the middle.
Ukraine enjoyed 73% possession of the ball in the first half, but struggled to find a way to break down the resolute Swedish defence, failing to register a single shot on target before the interval.
With so much still at stake, the second half started in frantic fashion - within five minutes of the restart, Anatoliy Trubin made an excellent reflex save to deny substitute Carl Starfelt from putting Sweden two up, before Gudmundsson saw a rapid strike flash narrowly wide of the target.
Straight down the other end, Serhiy Rebrov’s team finally recorded their first attempt on goal as Kristoffer Nordfeldt prevented Oleksandr Zubkov from finding an equaliser. With the contest increasingly stretched, a moment of class propelled the Blågult into a commanding position.
A long kick from Nordfeldt was latched onto by Gyokeres deep into Ukraine’s half, and the forward’s majestic finish into the bottom corner put Sweden on the brink of reaching the play-off final.
The match was all but wrapped up after 73 minutes, as the inspired Gyokeres broke free of the last defender before being brought down by Trubin inside the box.
The Premier League star took the spot-kick himself and, despite the goalkeeper going the right way, secured his hat-trick to put the Swedes out of sight.
With the game petering out, Ukraine managed to grab a consolation in the 90th minute as Matviy Ponomarenko headed home on his senior international debut to reduce the deficit to two before full-time.
Sweden’s vital victory ends a miserable run of six games without a win. Blagult will now face Albania for a place in the World Cup on the evening of Tuesday 31st, while Ukraine will play Poland in a friendly on the same night as their wait for a first finals appearance since 2006 goes on.