Laura Robson takes another giant stride with amazing win over Li Na to reach US Open round four

Laura Robson hits a return during her thriller with Li Na last night (Getty Images)

She will still be a teenager for another 16 months but Laura Robson yesterday completed the most stunning pair of results by a British woman for more than 40 years. Two days after sending Kim Clijsters, the three-time US Open champion, into retirement, Robson reached the fourth round of the year's final Grand Slam tournament by beating Li Na, winner of the 2011 French Open, 6-4, 6-7, 6-2.

In doing so Robson became the first British woman to beat two Grand Slam champions at a Grand Slam event since Virginia Wade accounted for Ann Jones and Billie Jean King at the US Open in 1968. On current form you would not bet against the 18-year-old knocking out a third in the next round, in which she faces Australia's Sam Stosur, the defending champion.

Robson, who is playing in the main draw of a Grand Slam tournament by dint of her world ranking for the first time, is also the first British woman to reach the last 16 of a Grand Slam tournament since Sam Smith made the fourth round at Wimbledon in 1998. Jo Durie was the last to play in the fourth round here, in 1991.

Yesterday's victory was every bit as remarkable as the win over Clijsters, who had not been beaten on these courts for nine years. Li, the world No 8 and a fine athlete and ball-striker, has been one of the form players of this summer. In winning the title at Cincinnati and reaching the final at Montreal, the 30-year-old Chinese had won nine matches in 11 days and beaten four top 10 opponents.

Robson, who had never previously claimed a top-10 scalp, has been on the British tennis radar ever since she won junior Wimbledon in 2008, but it is easy to forget that she is the youngest player in the world's top 100. Currently world No 88, she should climb at least 10 places to a career-high ranking at the end of this tournament.

"I've worked hard over the last few weeks and I feel like I'm playing very well," Robson said afterwards. "I have had lots of tough matches against some very experienced opponents, so the way that I see it, it was time to start winning a few of them."

Having beaten Clijsters in the cavernous Arthur Ashe Stadium, Robson faced a different challenge in the 10,000-capacity Louis Armstrong Stadium, which used to be the main show court here. The match started at 11am and on the hottest day of the tournament so far the temperature quickly climbed above 30C.

The power on Robson's serve and ground strokes has never been in doubt, but the improvement in her athleticism this summer has been extraordinary. She gets to many more balls than she used to and does so much more with them, denying her opponents easy points. Her new coach, Zeljko Krajan, has been encouraging her not to go for so many winners when she is at full stretch and to try instead to extend the points.

Robson looked composed from the very first point, when she struck a forehand winner down the line. Li, meanwhile, started with a double fault in the second game. With both players making early mistakes there were five breaks in the first set, the last of them when Li served at 4-5. A double fault and two missed forehands put Robson on set point and a backhand error finished the job.

The second set opened with another exchange of breaks, but as both players found their range on their serves and cut out their errors the contest became tighter. Li in particular was playing much better and from 3-1 down she took the tie-break 7-5, converting her first set point with a big forehand that caught Robson flat-footed on the baseline.

Robson, who had been within two points of victory, quickly regained the momentum in the decider, breaking to lead 3-2. The game featured one point that summed up her recent improvement. Sent scurrying from side to side by Li's ground strokes, Robson kept in the rally before hitting a superb forehand winner into the corner.

Another break two games later gave Robson the chance to serve for the match. Having gone 15-30 down with a double fault, she quickly regained her composure and converted her first match point after two hours and 25 minutes when Li hit a return long.

Robson's celebrity is clearly spreading. Wayne Rooney noted her performance on Twitter yesterday – even if he referred to her as "Robinson" – while Robson noticed James Corden in the crowd here. "I spotted him midway through the first set and then spent the rest of the time trying not to wave," Robson said.

Johanna Konta's attempt to give Britain two women in the third round of a Grand Slam tournament for the first time for 21 years had ended in narrow failure the previous evening when she was beaten 2-6, 6-2, 7-5 by Olga Govortsova, of Belarus. The former had lengthy treatment for a thigh problem in the second set, led 5-2 in the decider and served for the match twice but lost the last five games.

Konta, who was born in Australia but was given British citizenship this summer, should climb more than 40 places from her current position at No 203 in the world rankings following her performances here. "I think there's a lot of positives from this tournament for me," she said. "I think I'm heading in the right direction and picking up on things quickly."