No prizes are awarded for hitting top form in the third round but Britain's number two seed can be satisfied with the way he outplayed 29th ranked Robredo with his aggressive ball striking.
Murray broke for the first time in the third game of the first set against the number 32 seed and followed that with two more to close out the opener.
A rasping backhand pass delivered another break at the start of the second set and, apart from a brief moment of vulnerability as he was serving it out, the Scot never looked like relinquishing control.
The 31-year-old Robredo, who had never been past the third round in 12 appearances at Wimbledon, upped his aggression levels in the third set but found Murray's defences watertight.
Murray, aiming to become the first British man to win Wimbledon since 1936, broke in the 11th game and wrapped up the win when Robredo netted a backhand on his second match point.
Waiting for Murray will be the winner of the match between Russia's number 20 seed Mikhail Youzhny and Serbia's Viktor Troicki
