Montreal's Bouchard managed to find a way past Czech Karolina Pliskova 4-6, 6-4, 7-5 to win in her U.S. Open main draw debut. Dancevic, a product of Niagara Falls, Ont., defeated Robin Haase of the Netherlands 7-6 (5), 3-6, 7-5, 7-6 (7).
It was Dancevic's first victory in New York in four attempts after first-round losses in 2007, 2008 and 2011. Bouchard needed two hours 16 minutes to advance, with 26 winners and 32 unforced errors in her battle on hard court.
Rain ended Vasek Pospisil's match against Brazilian qualifier Rogerio Dutra Silva early. Pospisil missed on winning chances in the third set but left the court leading 6-4, 6-3, 6-7 (9), 0-4.
The Vernon, B.C., native appeared to have picked up a leg injury during the match.
The 19-year-old Bouchard, ranked 59th, lost the opening set on a break but rallied back to take the second set after 91 minutes on the court. Bouchard hung tough in the final set, closing out the tight victory with a break in the final game form a return long over the baseline.
"I was expecting good things for myself. I wanted to play and compete at my best," said Bouchard. "I didn't play that well, but I fought my hardest. I'm proud of that but I hope to improve for the next match. My serve was working the entire match, even at the end when it was tight.
"I was able to hold easily and put pressure on her. I felt fine at the end but I think she was getting tired. I was running for balls and broke her for 6-5. That was the key to the match. When I had my chances I tried to impose my game."
Dancevic, a qualifier who ranks 152nd, kept up his momentum in his four-set victory. The 28-year-old took a two-set-to-one lead and recovered in the fourth set after losing an early break against Haase.
Dancevic took it into a tiebreak, where he ran off a 4-0 lead before taking the victory on the third of four match points.
The Canadian jammed his toe on a shot and also scrapped his right elbow with a few dives on the hard court.
"I'm pretty happy with my performance today. I jammed the toe really bad in the second set and ended up cutting half of my toe nail off," Dancevic said. "I was struggling to move and worried about what might happen later in the match. I served better as the match went on, but we were both getting a bit tired in the fourth set and trying to win it on serve.
"The tiebreaks really made the difference, I played pretty well in them and that's what gave me the victory."
It was a late start for most of the Canadians in action, with only Toronto's Sharon Fichman on court early. The No. 95 Fichman was beaten by Romanian Sorana Cirstea, who lost the Roger Cup final this month to Serena Williams
Cirstea won the match 7-5, 5-7, 6-1 against Fichman.
Tenth seed Milos Raonic begins play on Tuesday against Italian qualifier Thomas Fabbiano.Suggest a correction