Shahar Peer breezed through to the third round of the Australian Open on Thursday, setting up a clash against world No. 4 Caroline Wozniacki.

After a sluggish start, Israel’s top female cruised through the first set but was made to work harder in the second before defeating Bulgarian Tsvetana Pironkova, 6-1, 6-4.

Although the pair had won two of their four previous encounters each, Peer, seeded 29th, took 81 minutes to outclass the unseeded Pironkova.

“I’m very happy,” Peer said after the match. “I’ve been playing a lot of matches [this year] and I’ve been playing well.”

The TV crews and heightened security detail that followed Peer’s first-round match on Wednesday amid unfounded fears of pro-Palestinian demonstrations did not appear to be present on Court 21.

Many of her usually raucous Israeli supporters seemed to have taken a siesta during the blistering midday heat in Melbourne as the mercury passed 30 degrees celsius.

Nonetheless, Peer was largely untroubled, despite losing her opening service game. She immediately broke back and, with the aid of a 73 per cent first service rate, won the next five consecutive games showcasing much the sublime form that saw her make the semifinal in Auckland a fortnight ago and the final in Hobart last week.

Although Pironkova appeared down, she was not out and, after losing her serve in the third game, broke back in the sixth game to level the set at 3-all.

Willed on by a small but vocal group of fans, the Bulgarian then held her serve to lead for the first time since the first game in the opening set.

But it was short-lived. The 22-year-old from Jerusalem – whose tennis career has earned her prize-money topping $2.5 m – broke back and at 5-4 served for the set.

The 22-year-old Bulgarian, ranked world No 111, stubbornly clung on, earning three break points. But Peer clawed back to deuce, before closing out the match on the second attempt.

Her next assignment, however, will be an entirely different proposition – a tough match against Wozniacki – in a reprise of their first-round match at the 2009 Australian Open, which Wozniacki won in straight sets.

“She’s a good player,” Peer said. “It’s going to be a tough match. She’s No. 4 in world and had a great year last year. But I’ll come and play my best tennis. I’m coming in to the match to win it.”

The pair has only met on one other occasion, which was also won by the Dane, who was runner-up in the 2009 US Open.

But they teamed up in doubles last year. “We’re good friends,” Peer said. “She’s a nice girl. I’m friends with her parents also, they’re a nice family.”

Despite, pre-tournament threats to protest Peer’s matches, an editor’s note posted on the Melbourne-based Australians for Palestine website on Thursday told supporters that they have been refused permission to protest in the vicinity of Melbourne Park.

“We're making other plans for protests [and] we will continue to post up signs around the city of Melbourne and will also continue to hand out flyers during peak periods.”

A poster on Peer on the site has a banner saying, “Shahar Peer serves for Apartheid Israel”.

It calls for a sports boycott against Israel, which it describes as an “apartheid state” that has imposed a “draconian siege” on Gaza.

Asked about the protests, Peer said: “Here there’s not anything happening. But in Auckland it was very tough on me, the things they were saying. I’m a tennis player and that’s what I’m here to do.”

Peer also won her doubles match just hours after finishing her singles match on Thursday. She and her partner, Kazakhstan’s Galina Voskoboeva, defeated Slovakia’s Magdalena Rybarikova and Czech Renata Voracova 6-2, 7-5.

Dudi Sela, who bowed out in the first round of the singles tournament on Tuesday, won his first-round doubles match with his partner, Russia’s Igor Kunitsyn, 6-4, 6-2.

Israel’s doubles supremo Andy Ram did not fare so well, going down with partner Michael Llodra from France 5-7, 6-3, 5-7 in the first round to France’s Julien Benneteau and Belgium’s Steve Darcis.

Ram’s former doubles partner Yoni Erlich progressed to the second round with his new partner, France’s Arnaud Clement. The pair defeated No. 10 seeds Julian Knowle and Robert Lindstedt in the first round, 6-7 (3), 6-4, 6-4.

It was Erlich’s first match at the Australian Open since winning the doubles title with Ram here in 2008.