One more win and Galal Yafai will become Great Britain's first boxer to win gold at the Tokyo Olympics.
The flyweight was involved in a war against Kazakhstan's Saken Bibossinov in the semi-finals but Yafai - who scored a standing count in the first round with a left hand - won 3-2 on the scorecards.
"I can't believe it. It's ridiculous, it's a dream," Yafai told BBC Sport.
"We're a close-knit team and we support each other. We have six medals now. It shows what GB Boxing is."
Price, the first Welsh female fighter at an Olympics, will face Nouchka Fontijn for a place in the middleweight final on Thursday.
Birmingham's Yafai wasted absolutely no time in asserting his authority at the Tokyo Olympics, with him easily overpowering Koryan Soghomonyan
Armenian Soghomonyan struggled to stay with Yafai, who was credited with three knockdowns before a stoppage in the third round.
He followed it up with wins against Zambia's Patrick Chinyemba and Cuba's Yosvany Veitia.
Can Yafai win gold? You bet he can, but he'll have to remain calm against a sharp Carlo Paalam.
The Filipino has defeated Ireland's Brendan Irvine, Algeria's Mohamed Flissi, Uzbekistan's Shakhobidin Zoirov and home favourite Ryomei Tanaka.
What day and time is it on?
The fight will take place on Saturday, August 7 and at 7.00 BST.