NEW YORK, NY, USA -- American CoCo Vandeweghe, the 20th seed, outplayed unseeded Ons Jabeur in a night match at the US Open on Thursday, eliminating the Tunisian, 7-6(6), 6-2, and advancing to the third round of her home Grand Slam for the very first time in her career.

"As I said in the oncourt interview, it's hard to beat a New York crowd when they're for you," Vandeweghe said, in her post-match press conference. "It's a lot to go against. That's what I was trying to make happen out there. I felt like I did."

"To be out there on Ashe and feel the energy, the vibe of it, was a lot of fun," Vandeweghe continued. "I had fun out there playing, competing. I think it definitely showed to everyone."

Jabeur had beaten Vandeweghe in their only previous meeting, in the final of an Challenger event in Canada in 2013.  The 23-year-old recently cracked the Top 100 for the first time in what is turning out to be her breakthrough season on the WTA.

But Vandeweghe is also riding high in her career-best season, sitting just outside the Top 10 in the Race to Singapore after a semifinal appearance at the Australian Open, the second Wimbledon quarterfinal of her career, and a run to the final of the Bank of the West Classic last month.

Jabeur showed off her court craft by utilizing her drop shot and slice backhand well in the first set, but she also possessed excellent service statistics in the opener, winning a higher percentage of second serve points than Vandeweghe did.

The American, meanwhile, won points with well-deployed volleys as well as the expected powerful forehands and serves.

This meant that there were no breaks of serve in the first set, as both players executed their game plans to success. Vandeweghe had the first look at 6-5, when she had three break points which doubled as set points, but Jabeur saved the first with a fantastic drop shot, and held from there.

"I think I was a little bit bummed out that I didn't get the 40-Love, 6-5 break," Vandeweghe admitted afterwards. "But, I mean, she hit some good shots and played well, to her credit."

In the first set tiebreak, Jabeur was very close to stunning the seeded player, when she hit a smash to go up a minibreak at 5-4, and then received a forehand error from Vandeweghe to give her two set points.

Vandeweghe's huge groundstrokes helped her to fend both off, and when she got to set point, a Jabuer error off the forehand side into the net gave the excited American a one-set lead.

"To be down in the tiebreaker and save some set points myself," said Vandeweghe, "I think that was a little bit of frustration and excitement just kind of being let out, energy being let out in that moment. Also showing her that I won the important set here because it was a tight first set."

The loss of the set indeed deflated Jabeur, and she swiftly lost her serve in the first game of the second set -- the first break of the match by either player.

The 25-year-old Vandeweghe broke again for 5-2 when a frustrated Jabeur hit an unforced error off of a slice backhand, which had been such a reliable shot in the opening set.

Too many unforced errors by Jabeur in the second set sealed her fate -- 14, compared to only six winners. Another Jabeur forehand into the net on Vandeweghe's first match point gave the American a straight-sets victory in one hour and 33 minutes.

In the third round, Vandeweghe will face an incredibly tough test against No.10 seed Agnieszka Radwanska of Poland. Radwanska has won five of their six previous meetings, all of those wins coming on hardcourts.