At 5-5 in the tiebreaker, Sharapova hit a cross-court backhand winner to earn a set point, which she quickly converted with an over-the-shoulder backhand volley winner off Mladenovic's lob. The Russian was in command the rest of the way.
Last year, Federer equaled Pete Sampras and William Renshaw with seven Wimbledon titles. He is now contending to become the first man to win the tournament eight times, which would bring his total of Grand Slam titles to 18.
Looking back on the last 10 years, Federer said he has continued to improve.
"Because I'm stronger, because I have the experience, because I've played so much, I'm just overall a more complete player," he said.
In keeping with tradition, Federer had the honor of playing the first match on the sport's biggest stage. This was the seventh time he strode out first on Centre Court.
"It's slightly different," he said. "Nine years ago when I came out the first time, it was the most special thing in the world. It still feels amazing. It was an absolute pleasure playing on Centre Court."
Federer came out wearing a white collared jacket with orange trim, then quickly got down to business. He never faced a break point and broke six times.
Federer has a habit of making things look easy. And so it was in the opening game when, stranded at the net, he reached behind him for a reflex forehand volley that landed in for a winner. In the third set, Federer lifted a perfect backhand lob over the 6-foot-6 Hanescu for a break and a 5-0 lead.
It didn't take long for Wimbledon to produce its first upset.
Puig slugged 38 winners in overwhelming Errani in the first match on Court 18. The 19-year-old Puig, playing her first grass-court tournament as a pro, completely outplayed the Italian veteran with her hard-hitting baseline game.