Murray also won in the doubles alongside Tim Henman

Murray, who had a bye in round one, won 6-3 6-3 and next plays Nicolas Mahut at around 2030 GMT on Monday.

He broke early in the first set and then again in game five of the second.

"I returned pretty good today," said Murray. "High percentage of first serves, didn't make too many unforced errors, so it was a solid match."

The Scot will next face Mahut after the Frenchman beat Russia's Marat Safin 6-3 4-6 6-0.

I had to return well and that's why I won so comfortably Andy Murray

Later on Sunday, Murray teamed up with Tim Henman for a 6-0 3-6 10-7 win over Argentines Juan Ignacio Chela and Sebastien Prieto in the doubles.

And Jamie Murray and American doubles partner Eric Butorac took their winning streak to 13 matches with a 7-6 7-5 win over Rafael Nadal and Feliciano Lopez.

In the singles, Andy Murray's quality of returning proved decisive as he saw off the big-serving Moodie.

The Scot converted his first break point in game four and grabbed the double break at the next opportunity.

Moodie got one of the breaks back but could not save the set and a pass down the line gave Murray break point in the fifth game of the second.

He failed to convert it but Moodie then double-faulted for Murray to break, and after earning triple match point in game nine he took the match at the third opportunity.

"These were my first matches outdoors for a while and the conditions are tough," said Murray.

"My win against Moodie was good because I knew it was going to be difficult and Moodie has such a big serve. I had to return well and that's why I won so comfortably.

"In matches like this it's important to play solid and not go too close to the lines and that's what I did. So this was a good test for me."