The 98-minute match saw the Frenchwoman start out by winning the first two games before Muguruza rattled off the next six games to ascend into a one-set lead.
Mladenovic would achieve the first break of the second set in the seventh game before the former world number one managed to claim the last three games to set up a second-round match with Aliaksandra Sasnovich.
Muguruza powers past Mladenovic with straight sets win
A blistering backhand brought up triple break point for Mladenovic in the very first game of the match and a netted backhand volley gave the Frenchwoman the early advantage, which she consolidated with a hold to go up 2-0.
After breaking back to even the score at 2-2, Muguruza watched as Mladenovic made a mess of a swinging forehand volley to go a break in front 4-2. Two games later, a double-fault handed the two-time major champion the opening set.
The second set was much more straightforward until the fifth game when Mladenovic failed to convert three break points and she bypassed two more in the seventh game, but had a third chance.
A forehand winner put the former top tenner in front 4-3, but she failed to sustain any momentum, giving the break back straightaway and after Muguruza saved a trio of break points in the next game, three double faults by Mladenovic handed the Spaniard the win.