Bauderlique, who lost 3-0 without any of the judges awarding him a round, will leave Rio with a bronze medal while La Cruz will fight either Britain's Joshua Buatsi or Kazakhstan's Adilbek Niyazymbetov for the gold.
Niyazymbetov won silver four years ago.
"I'm feeling good... I feel confident about the final," said the Cuban, who would be the first from a nation of champions to win light-heavy gold.
"I have to produce a really good performance but I think I will make it."
On a morning of quarter-finals, with 2012 Olympic heavyweight champion Anthony Joshua and retired professional Floyd Mayweather in the audience, eight bronze medals were decided.
The most controversial was the bantamweight bout between Irish world champion Michael Conlan and Russian Vladimir Nikitin, with the former beaten and blasting the judging and governing body AIBA.
Nikitin will fight Shakur Stevenson of the United States, a heavily fancied fighter that Mayweather is keeping a close eye on as a future professional prospect, who secured the second U.S. medal of the tournament.
Hopes of an immediate third medal disappeared when light-welterweight Gary Russell lost to Uzbekistan's Fazliddin Gaibnazarov, who will fight Russian Vitaly Dunaytsev in the semi-finals.
France's Tony Yoka secured at least a bronze in the super-heavyweight category after out-pointing Jordan's Hussein Iashaish 3-0.
Women's 2012 flyweight champion Nicola Adams opened the programme by shaking off some ring rust with a straightforward defeat of Ukraine's Tetyana Kob to ensure her second Olympic boxing medal.
(Reporting by Alan Baldwin, editing by Jan Harvey)
