Bale’s free-kick, which was turned into his own net by Ukrainian captain Andriy Yarmolenko, separated the sides despite the visitors dominating the game at the Cardiff City Stadium.
“The result is the greatest result in history of Welsh football,” said Bale, who previously led his country to the semi-finals of Euro 2016. “It’s what dreams are made of.
“I’m speechless because we’re so happy. We did it for all our amazing fans in the country. Words can’t describe our feelings at the moment.”
Ukraine made a nation proud in beating Scotland 3-1 on Wednesday in their first competitive clash since Russia’s invasion.
Oleksandr Petrakov’s men deserved much more from another exceptionally composed performance under the strain of carrying the hopes of a people devastated by Russian aggression.
“I think we did everything we could, but I really want the people in Ukraine to remember our team, our efforts,” said Petrakov.
“I want to say sorry we didn’t score but this is sport.”
The Ukrainian national anthem was applauded by all sides of the stadium before the game and, just as on their trip to Scotland in midweek, the visitors were inspired rather than inhibited by the pressure put upon them.
However, they were made to pay for some wayward finishing, one moment of misfortune and a heroic goalkeeping performance from Wayne Hennessey, who made nine saves.
“We gave everything today, we left everything on the pitch,” said Ukraine midfielder Oleksandr Zinchenko.
“The keeper from Wales did an unbelievable job. He’s definitely man of the match with his incredible saves.”
– Big game Bale –
Wales had barely threatened the Ukrainian goal in the first half, but in Bale have a star capable of changing the course of matches in an instant.
The 32-year-old is without a club having brought down the curtain on nine years at Real Madrid by picking up a fifth Champions League winner’s medal last weekend.
Bale has reserved his best for international duty in recent years and will now get the chance to add a World Cup to a glorious career.
His free-kick on 34 minutes was headed off target until Yarmolenko tried to head it to safety and only succeeded in deflecting the ball past the helpless Georgiy Bushchan.
“In big matches he delivered for us,” said Wales manager Rob Page.
“He did it against Austria (in the play-off semi-final) with two goals and he’s done it tonight with a free-kick. Somebody with that quality, he always poses a threat.”
Ukraine refused to be crushed by that misfortune and were unlucky not to be given a penalty before half-time when Yarmolenko was clipped by Joe Allen inside the box.
The pattern continued into the second half as Rob Page’s men were pinned back inside their own half.
But the home side did have big chances of their own to double their advantage on the counter-attack when Aaron Ramsey steered wide, Brennan Johnson hit the post and Bale shot meekly into the arms of Bushchan.
At the other end, chances continued to come and go as Viktor Tsygkanov’s effort was saved by Hennessey before Yaremchuk put the rebound wide.
A last-ditch challenge from Ben Davies then prevented Yarmolenko the shot at redemption.
Ukraine’s day was summed up five minutes from time when Hennessey produced an incredible save to prevent substitute Artem Dovbyk’s header finding the top corner.
But Wales are now unbeaten in 19 home games stretching back nearly four years for a reason as they were roared home by the majority of the 33,000 crowd.
Page’s men will face England, USA and Iran in the group stages in November.