The 27-year-old, playing his first match on grass since winning last year's Wimbledon title, looked totally at ease during a 6-4 6-4 victory to move into the third round of the Aegon Championships.
Also through to round three at the traditional Wimbledon warm-up tournament are top seed Stanislas Wawrinka and Frenchman Jo-Wilfried Tsonga, although surprise French Open semi-finalist Ernests Gulbis suffered defeat.
All eyes were on Murray, however, after his surprise decision to employ two-times grand slam champion Mauresmo as his new coach, following his split with Ivan Lendl who had steered him to the U.S. Open title followed by last year's historic triumph at the All England Club.
From the front row of the idyllic club close to London's West End, Mauresmo watched on intently as Murray strolled past his Mathieu to extend his winning run on grass to 19 matches.
Mauresmo applauded regularly and although not in the ilk of Murray's animated, fist-pumping mother Judy, she cut a notably different presence to that of the stern, expressionless Lendl.
"I just went on court with her the first time today," Murray, who will face Czech veteran Radek Stepanek next, told reporters. "This week there's not going to be any big changes in my game. I also wouldn't expect any before Wimbledon.
"But we'll definitely work on some things after the tournament is finished here."
Murray's decision to appoint a female coach, a rarity in top level tennis, surprised many but Murray said the pair had established an instant rapport.
"After I spoke to her the first time I just really liked her for a number of reasons," Murray said. "She was calm. She asked a lot of questions. She listened a lot.
"I liked chatting to her, so then I decided to sit down and speak to her and had a good chat about tennis, I spoke to her a bit about my team and things I wanted to work on.
"She was very easy to communicate with. I thought it would be a good time to try it out."
World number three Wawrinka, beaten in the first round at the French Open, probably would have preferred a little more match time on the grass on Wednesday but opponent Marcos Baghdatis lasted only five games before retiring hurt.
Tsonga beat Belgium's David Goffin 7-6 6-2 but Gulbis, who moved into the world's top 10 for the first time this week, lost to Kenny de Schepper 7-6(3) 7-5.
Four-times former Queen's champion Leyton Hewitt lost to Spanish left-hander Feliciano Lopez.
(Additional reporting and editing by Martyn Herman)
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