It was her second three-set match, having seen off world No. 2 Simona Halep on Monday in what was her first Grand Slam match since being hit with a 15-month doping ban a year ago.
If Maria Sharapova continues to play like she has in her first two matches at the US Open then there are not many players in the field capable of stopping her.
The Russian, US Open champion in 2006, paid the price for sloppy errors in the opening set, twice letting Babos off the hook immediately after breaking her serve.
Bouchard could only shake her head in the second set as she sprayed shots all over the court en route to 46 unforced errors in the first meeting between the players.
"I felt like it was a scrappy match but sometimes those days are the best, because you get through and give yourself another chance".
This was the second victory of Sharapova's return to the Open.
After her epic first-round victory over second seed Simona Halep, Sharapova was being touted by some pundits as a potential title contender.
But Kenin said she is still looking forward to the challenge of facing Sharapova, her childhood idol.
We've seen this before.
She is branded and nothing Maria Sharapova does on the tennis court for the rest of her career will erase the scarlet letter "M" (for Meldonium, not Maria) that she wears on her custom-designed outfits.
It had been 19 months since she had entered a major tournament. Paris declined the chance to hand her a free pass while NY laid out the red carpet. There's a certain level of 'I know I can do this. So Sharapova is the kind of big name the tournament needs.
Vandeweghe beat fellow countrywomen Alison Riske 2-6, 6-3, 6-4 elsewhere today while eighth seed Svetlana Kuznetsova of Russian Federation survived three match points before defeating Czech Republic's Marketa Vondrousova 4-6, 6-4, 7-6 (2).
"I definitely have to value the feeling that I have now". Sharapova hasn't lost before the fourth round of a grand slam since the 2013 Wimbledon.
The public here are well aware that Sharapova has spent most of her life in the United States.
"I think with the way that I played Monday night, I don't think there are any more questions", said the 30-year-old.
She rose and greeted Halep at the net, thanked the umpire, then battled back tears as she blew kisses to spectators, sobbed at times and mouthed "Thank you" to fans that were devoted throughout the two hour and 45 minute drama.
Blackman says that "you don't break Roger Federer 5-3 in the fifth unless you really believe that you can win that match, and that's something you can't teach". I felt it while I was away.
There were nothing but cheers from the crowd before, during and after Wednesday's win.
Venus Williams made short work of her second-round opponent at the US Open on Wednesday.
WWE Smackdown Live Results 8/29/17
Main event time, and with the numbers evened out it looked like the night would belong to Randy Orton and Shinsuke Nakamura . Orton hit the RKO on Nakamura as he celebrated after the match, the only storyline development for next week's main event.