The Wimbledon champion saw off Vincent Millot, the world No.267 from France, 6-2, 6-2, 7-5, winning the last 23 points from 5-1 down in the third set to clinch victory and a meeting with Spain's Feliciano Lopez.
However, the Scot admitted that seeing Jamie suffering from cramps hours after his first-round doubles match had left him concerned and had affected his focus. "It's easy to say, 'just get on with it; it's not that bad'," Murray said. "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. It is easy to say he was only playing doubles and it's not as physically demanding, but it's very tough conditions and seeing him like that . . . it wasn't so much he was cramping but that he was scared.
"He's never dealt with anything like that before and, being on your own, it's difficult, so I tried to make sure someone was around him the whole day."
In searing heat on a day that later topped 43°C, Jamie Murray and his Australian partner, John Peers, beat the all-Australian pairing of Luke Saville and Matt Reid 7-6, 7-6 in round one. "It started once the match had finished and I got back to the locker room," the elder Murray said. "I had a lot of ice treatment and then I was getting big cramps in my legs. I don't know what would have happened if we had gone into a third set but luckily that wasn't necessary. It wasn't too pleasant but I think I'll be feeling much better tomorrow."
The younger Murray said he had to adapt to cope with the heat."You just need to try not to use up any extra energy, no fist pumps," he said.
"I don't want to say you're not chasing down every ball but you're more thoughtful about how you play the points. That's all you can do."