Andy Murray did what he needed to yesterday – no more, no less – as he booked his place in the quarter-finals of the Sony Open with a 6-2, 6-4 victory over Italy's Andreas Seppi in Miami.

The Scot broke twice in the first set and survived a late push from the world No.19 to move into the last eight, another step closer to what he hopes will be a second ATP Tour title of 2013 and 26th in all.

Should he win the title on Sunday, Murray will replace Roger Federer as the world No.2 for the first time since 2009, but to do that, he will need to step up through the gears tomorrow when he plays the winner of last night's match between Jo-Wilfried Tsonga and Marin Cilic.

In his three matches so far, Murray has barely got out of third and yesterday he produced a few moments of class when required to dash any hopes Seppi had of extending the match to a third set.

"I think I started well," a satisfied Murray said after a third consecutive straight-sets win. "It was very windy on the court and swirling a little bit and he made more unforced errors than usual. I saw that after the first set, he hadn't hit a winner.

"He started going for his shots more in the second set and made it tough for me. I missed some returns on break points and he gained some confidence from that and he made it very difficult."

In truth, Seppi rarely looked like doing any damage, although he did have one chance to get back on serve when Murray was serving for the match only for the Scot to snuff out the chance.

In the first set, Murray looked sharp and Seppi's forehand, always his weak spot, let him down, first in the opening game as the world No.3 broke, and then again in the seventh, when he netted to trail 5-2.

Murray closed out the set with ease and should have broken the Italian early in the second but, to his credit, Seppi became more aggressive and held on.

The Italian actually beat Murray when they first met, on grass in 2006, but has lost all five meetings since. He has reached the top 20 thanks to a subtly effective game but his problem against the Murray of 2013 is simple; the Scot is better in every single aspect of the game.

At 3-4, Murray dug himself out of trouble from 0-30 and then, at 4-4, as the No.2 seed sensed his chance, the Italian missed two forehands to give him the break and he held on for victory.

Murray has always felt at home at Crandon Park – he has an apartment in Miami – and this week he has been accompanied by most of his family and both his dogs, Maggie and Rusty.

"It's been really nice," Murray said. "My brother was here, my dad's been here, my mum's here, my girlfriend's here and the dogs are here. It's nice to sleep in your own bed, I'm having a lot of fun here."

Another day, another drama for Serena Williams, though this time on the court rather than off it, after her bicycle dash through traffic before her third-round encounter.

This time, the world No.1 seemed to be struggling with a stomach injury against Li Na and trailed 5-2 in the second set after taking the first. But Williams refused to give in and stormed back to take the tie-break 7-5 and move into the semi-finals.