The 33-year-old Blake reached the tournament's second round for the second straight year.
Janowicz, ranked 16th, lost in his first appearance at the tournament. He lost to eventual champion Andy Murray in the Wimbledon semifinals.
"He's a really good player," Blake said of Janowicz. "I knew he could be a little up and down. He definitely didn't have his best first set.
"He started out a little slow, and I kind of took advantage, used the momentum, and it came down to taking really good care of my break points. I came up with some good serves and a couple of big forehands, and that was the difference, I think."
Stosur, who won the 2011 U.S. Open, lost in the round of 16 at the Rogers Cup in Toronto last week after winning the Southern California Open.
Williams was playing just her second match since losing in the first round of the French Open. She lost in the first round of the Rogers Cup at Toronto last week.
"I had a slow start," Williams said. "I was missing shots, but I was being aggressive, so I realized if I had made a few more that it would probably be the other way for me.
"She was really determined, I thought. She just looked really determined and really just energetic. She was definitely going to take it to me, so it was good to turn around and get a win. Feels good, yeah."
Ninth-seeded Angelique Kerber, who lost in last year's finals to Li Na, overcame losing a first-set tiebreaker before rolling through the last two sets in a 6-7 (6), 6-0, 6-1 win over qualifier Karin Knapp. American Sloane Stephens outlasted qualifier Petra Martic 6-2, 3-6, 6-3.
The top-ranked Williams, who won the Rogers Cup in Toronto, has never won the Western & Southern, losing in quarterfinals last year to the then-fifth-seeded Kerber.
"I'm motivated and happy and definitely feeling healthy," Williams said Monday.
The second-ranked Azarenka pulled out of the Rogers Cup last week to rest a sore back.
"I feel good," Azarenka said. "The first (tournament) back is always a little challenging to your body."
In men's play, Mardy Fish of the United States lost to 26th-ranked Philipp Kohlschreiber 7-5, 6-2. No. 32 Juan Monaco eliminated 33rd-ranked Jurgen Melzer 6-3, 6-2; 30th-ranked Jeremy Chardy beat qualifier Adrian Mannarino 6-4, 6-3. No. 20 Janko Tipsarevic bounced back from losing a first-set tiebreaker to defeat 28th-ranked Sam Querrey 6-7 (5), 6-3, 6-4.
"It's great to be back out there, for sure," said Baker, who played in a challenger event last week.
"That's number one. Second tournament back since January, you're always thankful to be back on the court."
In the first men's night session match, qualifier David Goffin ousted unranked American Mackenzie McDonald 6-1, 6-1.
Sharapova won the Western & Southern title in 2011.
The event is her first since losing in the second round at Wimbledon. She's also been bothered by a hip injury.
"Everything is feeling fine," the third-ranked Sharapova said. "I'm at the stage of my career where I have the luxury of making sure. I love playing a full schedule, but I'd rather come in here feeling good and healthy. I haven't played in weeks, so I might be a little rusty."