Host nation heavyweight (91kg) Abdulkadir Abdullayev scored a unanimous quarter-final points victory over Paul Omba Biongolo of France, while compatriot Souleymane Cissokho also missed out on a semi-final spot, narrowly losing his welterweight (69kg) bout against Russia's Alexander Besputin.
Both boxers needed treatment for cuts, and the Russian, who sustained his in the previous fight, must now carry his injury into his semi-final against Ukraine's Yaroslav Samofalov on Friday.
Frenchwoman Estelle Mossely, the woman who claims she knows how to beat Ireland's multiple gold medallist Katie Taylor, remained on course to put her theory to the test, however, when she beat Italian soldier Romina Marenda in the quarter-final of the lightweight (57-60kg) competition.
Sandy Ryan of Great Britain pulled off an unexpected victory when she beat the home country's Elena Vystropova on a split decision in the light-welterweight (60-64kg) class, meanwhile, assuring the British women's team of their first medal.
Ryan did not expect to be in Baku after suffering an injury last year.
She said: "I had a stress fracture in my right leg. I was training a lot and only coming home at weekends. I should have been resting and I wasn't.
"I thought that the European Games would have been out, but I got back about five, six weeks ago and I have trained so hard for it.
"It definitely puts me on the world stage, and nobody wants to be there more than me."
Ryan will meet Russian Anastasia Beliakova in the semi-finals, and will be looking for revenge against the boxer who beat her last year in the world championship gold medal bout in Jeju City.
A British-Irish match led to Team GB's stylish welterweight Josh Kelly coming out marginally on top against Adam Nolan to guarantee his first medal in major competition.
He now meets the no.2 seed, Azerbaijan's Parviz Baghirov who, despite being cut, claimed a unanimous points victory over Abass Baraou of Germany.
A third Azerbaijani to go through to the semi-finals was Cuban-born Collazo Sotomayor, who made the most of his long reach to outpoint rugged Daniel Niculescu of Romania in the light welterweight (64kg) quarter-final. He now meets Ukrainian Viktor Petrov in the last four.