The No. 4 seed has yet to drop a set in the tournament, which bodes well for later rounds.
It was a commanding performance from Murray and he will now face lucky loser Stephane Robert.
It started poorly for Murray, however, with an uncertain service game that saw Feliciano Lopez go into an early lead. Although Murray broke back immediately and then followed up with a dominant service game of his own, he looked a little uneasy on court.
ESPN previously reported that Murray had trouble concentrating during his second-round match as his mind was on his brother. Jamie Murray had collapsed with heatstroke during his doubles game and Andy admitted that his thoughts were elsewhere:
What was happening with Jamie was more important than my match. It was a little distracting as well and you just try not use up any extra energy.
It's easy to say: "just get on with it, it's not that bad." But when it's someone in your family who is dealing with it, it's their health that is involved, you see that it's fairly serious, it's different.
Perhaps his thoughts again lingered on his brother as Lopez took that first game and Murray looked a little distracted at times during the whole of the first set. He was 0-30 in his third service game before waking up to claw his way back into it and was often fortunate to remain in the set as Lopez fought a battle with his own net cord.
Nevertheless, Murray took control of the resulting tiebreak with a deft drop shot and a powerful smash, amassing a 4-1 lead that Lopez couldn't overcome.
From there it was all Murray and he broke Lopez in the opening game of the following two sets. The Spaniard frustrated both the crowd and himself with flashes of brilliance followed by utter mediocrity, and Murray seized the opportunity.
With a quick double break in the third set, the result was assured. Lopez cut a dejected figure as his opponent could suddenly do no wrong, bouncing around the court, aided by a cool breeze and finding the corners of the court at will.
Every player is looking to get off court as soon as possible this year. Energy must be preserved to prevent exhaustion as the temperatures rise. Murray did exactly that, overcoming some early indecision and finding his game when it really mattered.
A victory on all fronts, then.