He faces France's Adrian Mannarino.
The world's top tennis stars all have their tricks to help them bounce back after tough stretches, but Canada's Eugenie Bouchard may still be looking for one that works for her.
A former champion in Montreal, Caroline Wozniacki snagged her first-ever win in Toronto with a 6-3, 6-0 victory over Ekaterina Alexandrova in the second round of the Rogers Cup on Tuesday night.
Vekic won her spot in the main draw via a two-round qualifying tournament over the weekend.
"Most people think that if you win a Grand Slam, you know, you have that extra confidence, so much confidence that you're going to win matches by miracle". So it's tough to get through tough matches when you're in a moment like that.
Despite the fact she doesn't have a lot of experience on the WTA - Tuesday's was her 62nd match on tour - she tried to treat this match like any other. But she also isn't playing much. Each player held serve over the next five games before Bouchard hit the net down 40-30 to give Vekic the match.
The wild card, ranked 70th in the world, was unable to beat qualifier Donna Vekic, who progressed 6-3 6-4. "I want to kind of play free", said Bouchard, who has been inspired by some recent training sessions with the great Andre Agassi.
The 17-year-old Andreescu, ranked 144th in the world, was the last remaining Canadian in the women's singles draw.
Bouchard will continue her doubles campaign on Thursday when her and Plíšková will take on Anna-Lena Groenefeld and Kveta Peschke in the second round. And I think it's important to feel the pressure of time a little bit, to get into action and not just relax and let years go by. "I practised with her a little bit last week in D.C., and I think she had a good run last week". It is good to see that someone else can carry the burden in Canada... So I've got to be ready for her.
Yes and no. I mean, I guess I'm relatively young, but I feel old in a way. "I knew that if I played decent tennis my ranking was going to go up again". That would be the worst thing I could do.
"I love to try to put on a show for the crowd", Andreescu said shortly after the loss, referring to that long point.
She was broken six times by the 21-year-old Vekic, who is in the main draw of this US Open tuneup for the first time.
It wasn't all bad news for Bouchard on Tuesday, though.
But, as the skies turned dark and heavy and the rain came down at a brightly lit centre court, the American veteran's match against a game Romanian in world No. 38 Irina-Camelia Begu was suspended with Williams up 2-1 in the third set.
Bouchard said she made a decision to play doubles to "get a little more match play" in this otherwise match-deprived season. To me, even if it's doubles, and I generally am more of a singles player, it's still pressure of a match, and better than practice and more fun than practice.
She lost her serve early in the second, and didn't win a game until she was down 5-0.
Caroline Garcia, CiCi Bellis, Barbora Strycova, Anastasia Pavlyuchenkova, Elena Vesnina, Ashleigh Barty and Magdalena Rybarikova were also first-round victors.