The Spaniards, who finished runners-up to the United States at the 2012 Olympics, will play either hosts Slovenia or France for a berth in Sunday's final.
The Slovenians and the French lock horns later on Wednesday (1900 GMT), while Croatia take on underdogs Ukraine and 2003 winners Lithuania meet Italy on Thursday in the other two quarter-finals.
Spain lost three matches in the two preliminary group stages after playing in fits and starts but hit top gear against the Serbians, romping to a 21-5 lead in the first quarter thanks to 13 points from Fernandez.
Rodriguez added 14 in the second period and initial cheers of support by 8,000 Serbian fans for their team in the Stozice arena turned into jeers midway through the third quarter, when a Ricky Rubio three-pointer gave the defending champions a staggering 69-29 advantage.
Serbia restored some respectability to the scoreline late on but it was scant consolation with their worst performance in the 24-team tournament having come on the back of impressive wins over Lithuania and France.
Rodriguez led all scorers with 22 points, Fernandez added 19, while guard Danilo Andjusic and centre Rasko Katic netted 11 each for Serbia.
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