Some metal surfaces are often unable to be contacted effectively with fluids containing hydrofluoric acid or acidic fluoride ions due to significant corrosion issues. Metal surfaces comprising titanium or a titanium alloy represent but one example. Corrosion inhibitor compositions comprising boric acid and other boron-containing compounds may at least partially suppress corrosion of titanium and titanium alloy surfaces. Methods for suppressing corrosion may comprise: introducing a treatment fluid comprising hydrofluoric acid or a hydrofluoric acid-generating compound to a subterranean formation; forming an at least partially spent treatment fluid in the subterranean formation; adding a corrosion inhibitor composition comprising a boron-containing compound to the subterranean formation, thereby forming an inhibited, at least partially spent treatment fluid in the subterranean formation; and contacting the inhibited, at least partially spent treatment fluid with a metal surface comprising titanium or a titanium alloy.