The pair played the game in an amusing manner with many net rallies and a huge variety of shot selection on both sides of the court.
In the opener Murray made the break in game three and went on to take the set 6-4 thanks to some consistent serving.
Frenchman Llodra struggled with injury problems in the second, calling a timeout midway through the set as Murray began to take control.
Some of the tennis on show was rare for a Grand Slam with Llodra winning a point in the final game of the set by playing the ball around the net post. These entertaining passages of play were not enough to stop Murray, who claimed the second 6-2.
Heading into the third, the Scot had already won three games in a row and went on to claim the next six, winning the set to-love.
The unseeded Mikhail Kukushkin awaits Murray in the last 16 after the Kazakhstani surprised 14th seed Gael Monfils in a five-set encounter.