Mature Heather Watson cutting out elementary mistakes

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They still have a long way to go before their achievements can be mentioned in the same breath as those of their predecessors from the 1960s and 1970s, but Laura Robson and Heather Watson are putting British women's tennis back on the map in a manner that promises the brightest of futures.

Here tonight (mid-morning UK time), Robson will follow Roger Federer on to the stage in the Rod Laver Arena to play the final match of the main night session at the Australian Open against Petra Kvitova, the 2011 Wimbledon champion.

Tomorrow Watson, having saved three match points in a thrilling three-hour victory yesterday over Ksenia Pervak, will take on Agnieszka Radwanska, the world No 4 and last year's Wimbledon runner-up.

It might be tempting to suggest that it cannot get much better than that, but at their current rate of progress the 18-year-old Robson and 20-year-old Watson should have many even greater days ahead of them.

If Robson wins today – a tall order, nevertheless, given that Kvitova is the world No 8 – Britain will have two women going through to the third round of a Grand Slam tournament for the first time since Jo Durie and Sara Gomer reached the last 32 at the US Open in 1991.

While Robson, with her big-hitting game, remains the better long-term prospect, Watson demonstrated once again what a feisty competitor she is. The world No 50 struggled with the wind and with her game against the consistent Pervak and she was on the brink of going out when the 21-year-old from Kazakhstan set up three match points by taking a 6-3 lead in the second-set tie-break, Watson having lost the previous two points with unforced errors.

Watson, however, gritted her teeth and told herself that she would put every ball back in play and make Pervak earn her victory. On the first match point Watson won a 28-shot rally, the longest of the match, and eventually forced Pervak into three successive errors with the strength of her defence before going on to win the tie-break 9-7.

Pervak's spirit was broken in the deciding set, though Watson still had to cope with cramp before winning the match 4-6, 7-6, 6-2. Having played tentatively for most of the first two sets, Watson was much more effective when she went for her shots in the latter stages.

Watson hugged supporters at the end and spent several minutes posing for photographs and signing autographs, having enjoyed raucous backing from the crowd on No 8 Court.

"Thank you so much, I couldn't have done it without you," she told the fans before adding: "They were awesome throughout the whole match. It's easy to support someone when they're winning, but when they're losing it's not as easy. They were just non-stop from beginning to end supporting me – and it was just unbelievable being out there."

On her only previous meeting with Radwanska, on Centre Court at Wimbledon in last year's third round, Watson managed to win just two games. "That killed me," she recalled. "I was so upset. I was playing at home in front of everyone and I just got wiped off the court. That wasn't a great experience. I just went guns blazing. I didn't know what to do and I just went for way too much.

"This time I'm coming in a different player and I'm going to approach it differently. I feel more experienced. I feel more confident in my game. This is my second third round now [in a Grand Slam], so I've been here before."

Since that Wimbledon meeting Watson has won her first title on the main tour and broken into the world's top 50. However, in Radwanska she will be facing an opponent who is at the top of her game. The 23-year-old Pole began 2013 by winning titles in Auckland and Sydney and has won all 11 of her matches this year without dropping a set.

Mauricio Hadad, Watson's coach, has been trying to encourage the British No 1 to play a more aggressive game. "She's new to the tour, relatively, only a year on the full tour, and she has to work on hitting the ball, and that's what she started on from day one," he said. "She has got better but she can do a lot better and can hit the ball from the very first moment.

"As she grows older and gets more mature and more confidence in herself and the way she needs to play to beat the top girls, she will continue to do it," Hadad added. "She is starting to understand how and when to hit the ball hard and how to keep the ball in play and use her biggest asset, which is her footwork. The way she runs, it's very difficult to get the ball past her. She needs to continue to work the same way.

"Before, she had a hard time coming to the net. Now she's coming to the net when the ball is up in the air and taking it, which is something we've worked on, because she'll have to do that more in the next years if she's going to be really successful.

"She won't blow players off the court with her groundstrokes because she's not that big and her shots aren't that huge, so she has to come up to the net and finish the points."

Robson, meanwhile, has played in the Rod Laver Arena twice before, in junior finals, and described the prospect of following Federer on to the court for the climax of today's night session as "pretty cool". She added: "I think it's easy to play on a big court with a big crowd when you have nothing to lose. It's enjoyable."

Playing in the heat of the day might have been more to Robson's advantage – the temperature was forecast to climb to 39C today and Kvitova, who suffers from asthma, sometimes struggles in testing conditions – but Robson, the 2008 Wimbledon junior champion, proved with her victories over Kim Clijsters and Li Na at last year's US Open that she is a player for the big occasion.

"I'm just going to try and play my own game," Robson said. "If I get sucked into defending all of her shots all of the time, that is not going to work out very well for me. I've got to stay aggressive and just play as well as I can really. It's going to be really tough."