Meusburger won 6-0, 6-2 to avenge their only other previous meeting, which Cabeza Candela won in straight sets in 2012.
Meusburger lined up her second straight quarterfinal on tour against Romina Oprandi, after the Swiss player defeated Beatriz Garcia Vidagany of Spain, 6-2, 5-7, 6-2 in a match which saw 13 breaks of serve.
Oprandi secured eight of them against Vidagany, who beat defending champion Francesca Schiavone in the first round.
There was better news for another Spaniard, as Maria-Teresa Torro-Flor eased past compatriot Lara Arruabarrena 6-1, 6-2.
She will next face Polona Hercog of Slovenia, who beat Alison Van Uytvanck of Belgium, 6-1, 6-4.