NEW YORK—There was no hiding today on Louis Armstrong Stadium, not for the fans in the seats on a toasty day, or Agnieszka Radwanska along the baseline, her comfort zone on the court. For while visors and sunscreen could only negate the sun’s intensity, the No. 4 seed’s backhands could only delay the inevitable: Peng Shuai was simply stronger. The world No. 39 beat Radwanska at her own game, using her backhand and all-court savvy to great effect in a 6-3, 6-4 second-round upset.

The highest seed to fall thus far at Flushing Meadows, Radwanska was engaged in a baseline battle from the beginning. Her short backswings were countered by Peng’s similarly struck two-handers—both on the forehand and backhand side. But Peng’s uniformity in delivery contrasted with her variety in execution. The backhand was her bread-and-butter shot, but with it she mixed flat, vertical drives with curling, cross-court jabs. When forced to hit a forehand—Peng often ran around that side—she imparted top spin to change the tone of a rally.

Radwanska dropped the first set partly due to Peng’s high level of play and partly due to her own stubbornness. Backhand-to-backhand exchanges usually end in Radwanska’s favor, but not on this day. By the latter portion of the second set, Peng held the edge in backhand winners, 12 to four, while Radwanska was making costly mistakes, despite hitting just 19 unforced errors on the day.

The Pole’s biggest problem, though, was her break point conversion. She was just one of seven overall, and a few stick out. After three holds to open the second set, Radwanska reached 15-40 on Peng’s serve. She couldn’t do anything on the first chance, as Peng followed her double fault with an ace. But Radwanska let Peng off the hook on her second break point of the game, then bailed out of a baseline rally with a woefully short drop shot at deuce. Peng held, and the pressure immediately shifted to Radwanska at 2-2.

Radwanska couldn’t handle it—or, more precisely, couldn’t handle Peng. Battalions of balls were sent toward (and away from) Radwanska, who could never dispel Peng for an extended stretch of time. It didn’t help that Radwanska’s serve was attacked as well. On Peng’s break chance at 30-40—earned by opening up the court for a down-the-line backhand blast—she punished Radwanska’s serve with a backhand swipe. The shot wasn’t returned, and Peng led by a set and a break.

While Peng had opportunities to extend her lead and Radwanska had opportunities to claw her way back, the prevailing sense was that the unseeded baseliner had the upper hand throughout. But she’d still need to serve it out, an entirely different obstacle.

“One time at Australian Open I had two match points and didn’t make it,” Peng said afterward, referring to their 2011 fourth-rounder she lost, 7-5, 3-6, 7-5.

She did today, but not before letting two more match points slip away. The first was earned on Radwanska’s serve, at 5-3, with a brilliant running forehand winner. The second was earned on her serve, at 5-4, with a brilliant backhand swing-volley winner. In both cases, backhand errors kept Radwanska alive.

But as was emblematic of her entire day, Peng kept up the “fight,” a word she uttered repeatedly in the on-court interview. In this entertaining and relatively clean match, it was appropriate to see Peng earn her third match point with a backhand winner, and secure the upset with another backhand that Radwanska could only watch sail by.