Two novel ternary compounds, yttrium borate oC20-YBO3 and yttrium orthocarbonate hR39-Y3(CO4)2, were synthesized at 90 and 120 GPa upon heating to about 3500 K in a laser-heated diamond anvil cell. Their crystal structures were solved and refined using in situ high-pressure synchrotron single-crystal X-ray diffraction. The crystal structure of oC20-YBO3 features previously unobserved infinite unbranched zigzag chains of corner-sharing BO4 tetrahedra. The compound hR39-Y3(CO4)2 consists of isolated [CO4]4- orthocarbonate anions and represents the first rare-earth orthocarbonate. Density functional theory calculations reproduce the structures of the new compounds and provide further insight into their stability and physical properties. Our results enrich the chemistry of metal borates and carbonates.