Phau had accounted for Wimbledon giant killer Lukas Rosol earlier in the tournament, but the world number eight battled back after losing a first-set tie-break to progress.
The Serb will next face Brazil's Thomas Bellucci, who beat Germany's Cedrik-Marcel Stebe 6-4 6-1 in the last match of the day.
Earlier in the day second seed Juan Monaco was the first man through to the semi-finals after downing Pavol Cervenak 6-1 7-5.
The Slovak qualifier had upset veteran Tommy Haas in the previous round, but Monaco proved a class above.
The Argentine only sent down two aces in a match which saw 11 breaks of serve, but took his opportunities when receiving to seal the match in 96 minutes.
Monaco's semi-final opponent will be Spain's Guillermo Garcia-Lopez, who eased past Germany's Dustin Brown 6-0 6-3.