The Swiss world No20 rallied back from a set down to upset Radwanska 2-6, 6-4, 6-2 in two hours and two minutes, and make the last eight in the Premier Mandatory event in Florida for the first time.

Radwanska, a champion in Miami in 2012, showed her signature variety to race to a one set lead, hitting a mere seven unforced errors.

The Pole trailed by a break in the second and despite breaking Bacsinszky back when the Swiss was serving for the set at 5-3, she surrendered her serve once again and lost her advantage.

Bacsinszky did not look back from then on, benefitting from a slew of Radwanska errors to wrap up her first-ever top-three victory.

“Even when I wasn’t playing quite well in the first set, I told myself, it might be a long match,” said Bacsinszky, who last year made her top-10 debut in October.

“So I always tried to get a little more balls in and make her work.

“But I started to calm down a little bit – in the first set I was kind of nervous.”

Bacsinszky, who had taken out Ana Ivanovic in the previous round next faces world No5 Simona Halep, who got past an in-form Heather Watson 6-3, 6-4 in the last 16 Monday.

Halep dropped her first two service games against Watson to trail 1-3 but rallied back, winning the next five straight games to take the opener.

Great Britain’s Watson, currently ranked 69th in the world, was then broken again in the fifth game of the second set before breaking back to make it 3-3.

But yet another break put Halep 4-3 up before the pair held serve to give the Romanian the chance to serve for the match. The 2014 French Open finalist then wrapped up the win with a love service game to advance into the quarter-finals and take her record against Watson to a clean 3-0.

Halep’s best result in Miami was making the semi-finals last year.