Murray said he got a good workout against number 36 Chardy, who won the Stuttgart clay title last month.
'I started well and every time I was in a tough situation I came up with some big serves and some big shots. That was the difference.'
'There were a lot of tough moments,' said Murray. 'I saw 10, 11 break points. That's always good when you come back. That was the thing I was most pleased with ... in the tight moments I came up with some big shots.'
Murray awaits the winner from 13th seed Gael Monfils and former french Open champion Juan Carlos Ferrero.
The Spaniard, whose career is taking off once again at age 29, defeated fellow former number one Lleyton Hewitt 6-1, 6-4, with the Australian still suffering with a muscle tear from last week in Washington.
In other first-round contests on a day featuring both humid sunshine and an afternoon rainstorm, Spanish 15th seed Tommy Robredo beat American qualifier Alex Bogomolov 6-4, 6-2 .
Philipp Kohlschreiber and Tommy Haas doubled up for Germany, with 'Kohli' defeating Czech Tomas Berdych 7-6 (7-5), 6-7 (9-11), 6-4 and Haas recovering to defeat Croatian serving machine Ivo Karlovic 4-6, 7-6 (7-3), 6-4.