MELBOURNE, Australia – Serena Williams attacked Maria Sharapova's strength, and it helped extend her complete domination of their rivalry, earning the six-time Australian Open champion a place in the semifinals.

The top-ranked Williams beat Sharapova 6-4, 6-1 in the quarterfinals Tuesday, her 18th consecutive victory and 19th in their 21 career meetings back to 2004.

"It was super intense," Williams said of the replay of last year's final. "She's an incredibly intense, focused player who was No. 1 and has won so many Grand Slams for a reason. You have to come out with a lot of fire and intensity."

Each of the six previous times Williams has won a quarterfinal at Melbourne Park, she has won the title at the season-opening Grand Slam tournament.

Up next for her is fourth-seeded Agnieszka Radwanska, who beat No. 10 Carla Suarez Navarro 6-1, 6-3 to reach a Grand Slam semifinal for the fifth time.

Sharapova has won five majors, including the 2008 Australian title, and has been in three other finals at Melbourne Park.

In her fourth-round win against No. 12 Belinda Bencic she had a career-high 21 aces. Against Williams, she had three, and seven double-faults.

Williams had 13 aces, three double-faults, hit 31 winners to 11, and broke Sharapova's serve four times.

"She played quite explosive," Sharapova said. "She was really explosive off the return. Yeah."

Sharapova broke to open the match and held for a 2-0 lead. But Williams held in the third game and broke to quickly level at 2-2.

Early in the set, points were short. As it progressed, the rallies got longer, the shrieks and grunts got louder and the emotions were fully on display.

Both players struggled with their ball toss at one end, repeatedly practicing their toss to work out the best position to serve into the sun.

Williams also had to concentrate hard to hold in the ninth game, when a baby screamed loudly in the stands as she faced breakpoints.

She was able to protect her own serve, and go on the attack against Sharapova's. It cost her in the eighth game when she had three break-point chances, taking the high-risk shot rather than the high-percentage option with her return.

But that approach is what has helped win her 21 major titles, and Williams' aggressive returns finally helped her convert on her fourth set point, following a heavy ground stroke to the net and putting away a volley.

She went on a five-game roll until Sharapova held in the second set, and then finished it off in the seventh game after saving break points.

Williams had medical treatment between sets, and again in the second during a changeover, but it wasn't clear what the problem was. She didn't comment on it in her on-court interview.

Sharapova noted Williams started the opening set with four big serves, so she didn't think it hampered the 34-year-old American's game.

She hasn't beaten Williams since back-to-back victories in 2004, when she led their rivalry 2-1.

Despite more than 11 years in between, Sharapova isn't giving up hope of breaking that drought.

"It's motivating because she's at a different level," Sharapova said. "She makes you go back to the drawing board, not just for me, but for many other players. She makes you work. That's inspiring."