Good signs for last year's Australian Open bolter Sloane Stephens Clinical win .. Sloane Stephens fires a return against Alize Cornet. Sloane Stephens enjoyed a fantastic 2013 and if her Hopman Cup form is any indication, 2014 is looking good also. The 20-year-old American, who memorably reached last year's Australian Open semis, breezed past France's world number 27 Alize Cornet 7-5 6-0 at Perth Arena. It was the pair's first look at one another, but once Stephens found her feet, there was no holding back. Even in the first set Cornet was forced to serve a lot of balls. Her opening service game went nine minutes and she saved one break point. Cornet then served 45 balls and faced 10 break points during the second set. I definitely played solid in the second set. It is not often I win a set 6-0 so I was proud of myself for that. I stayed tough," Stephens said. At this point playing at all is good preparation. I knew I just had to up my game a little bit to be able to stick it to her a little bit. I just tried to stay solid and stick to my patterns. It started off a little shaky but it ended up pretty good I thought. Earlier in the tournament, Stephens beat Spain's Anabel Medina Garrigues 6-3 6-1. This time last year Stephens had a solid start to her 2013 campaign. She was beaten by Serena Williams in the quarter-final in Brisbane and then by Russia's Elena Vesnina in the semi-final in Hobart. She was ranked 25 going in to the Australian Open, but was one of the surprise packets of the tournament by winning through to the semi-final, beating Williams in the quarter-final in three sets. But world No.1 Victoria Azarenka was too good next up, winning 6-1 6-4 before going on to claim the Australian Open. Cornet, 23, said Stephens was a tough opponent to hit winners against. "All credit to her; she is very solid, she runs very well, moves very well, tough to make winners," the Frenchwoman said. She is doing everything good; her forehand is a real winner. Cornet is yet to win a match at the Hopman Cup, having lost to the Czech Republic's Petra Kvitova on Monday. But she is very keen to gain some momentum after struggling in Australia last summer. She was bundled out of Hobart in the first round and made it only one match further in both Brisbane and the Australian Open, losing to Serena and Venus Williams respectively. "I was feeling well for the match; Sloane was just better," Cornet said. Yeah, the first set was very good from both of us. The second set was quite good. I had a lot of game points and I didn't make any of them. When you have to take 15 minutes to win a service game, it is quite tough. Yeah I was very disappointed with my first match, but happy with my level. When you leave the court and it is 6-0. you are not very happy. I will try to get the positive out of it, but tonight I think I could have done better.