She, however, has a risky first-round opponent in Japan's Naomi Osaka, who emerged as the surprise victor at Indian Wells.
The player Cahill coaches - world No. 1 Simona Halep - added that Williams should have been the top seed in Indian Wells because after she contested her last tournament before stepping away from the game, she was ranked No. 1.
The world No.22 broke Williams again after a back-and-forth deuce battle to take the first set.
Williams had to save break point in her first service game of the second set, a thumping serve down the middle helping her to hold.
Osaka, 20, won her first professional singles title Sunday with her 6-4, 6-2 win over Daria Kasatkina.
The British No 1 has won only eight matches since her run to the Wimbledon semi-finals previous year but will hope the positive memories from her title-winning run can bring about a strong defence.
Had Williams been seeded using her protected ranking of 22nd in Miami - Osaka ironically is now ranked 22nd - she would have benefited from a bye in the first round and not met another seed until the third round at the earliest.
Resurgent Del Potro returns to the top with Indian…
Federer does not have long to cool down, however, as he is set to compete in the Miami Open, which starts Monday. According to the tournament's website , Federer said he "has to get over" the loss.
Because of her maternity leave, the 36-year-old returned to action as an unranked player and will remain unseeded for Women's Tennis Association (WTA) events. That was her best ever result in Florida, but now returning as reigning WTA Finals and Australian Open champion, she will surely be confident of going one better.
Williams is an eight-time Miami Open victor, but she can't be seeded due to the fact that she's unranked.
'It makes sense to protect someone who goes on maternity leave, ' said Blake about his countrywoman. But late Monday night, the 23-time Grand Slam singles victor (and new mom) realized that something about the Nickelodeon show never quite made sense to her: "if the original benders were sky bisons, badger moles, and dragons; how does that tie in with Avatar Wan when the lion sea turtle gave all the people bending power?" "I'm getting there. It's not exactly where I want to be, but I'll get there eventually".
Williams had an especially hard time after giving birth in an emergency C-section, with her past issues with blood clots resurfacing because having surgery meant she was not taking her usual anticoagulant. Both can hit a huge ball, but also move well, making this a potentially thrilling clash. How is Naomi going to react to winning her first big title?
"So just playing against her is kind of like a dream for me". I told you, I need a CT scan and a heparin drip, ' she remembers telling the team.
Serena's coach Patrick Mouratoglou, who has been by her side for almost six years now, has identified the three remaining Grand Slams of the year as Serena's major targets.