Serena Williams of the U.S. reacts after winning the first set against her compatriot Madison Keys during their semifinal match at the Australian Open tennis championship.

MELBOURNE, Australia — Serena Williams came up with a big service winner to close out the tiebreaker, and bounced around behind the baseline like she’d won a title.

After holding on to win the tough first set against 19-year-old Madison Keys, prompting the early celebrations, the 18-time Grand Slam champion dominated the second set in a 7-6 (5), 6-2 victory to move into an Australian Open final against second-seeded Maria Sharapova.

It’s the first time since 2004 that the top two seeds will meet in the women’s final at Melbourne Park.

The 33-year-old Williams, who has won all five times she’s reached the Australian Open final, will be the oldest player to reach the championships match in Australia in the Open era.

Sharapova won the 2008 title, but was comprehensively outplayed in her two other trips to the final — by Williams in 2007 and by Victoria Azarenka in 2012.

Williams, who has been struggled with a cold for a week, said she’d recover from a tough workout in the all-American semifinal against Keys, who pounded her with heavy groundstrokes and a big serve for the first set.

“She pushed me really hard the first set ... and I had to really dig deep mentally to get through that,” Williams said. “It was a little frustrating. I had like nine or 10 match points and couldn’t close it out. That doesn’t happen so much. She played like she didn’t have anything to lose.”

Keys, playing in her first Grand Slam semifinal, saved seven match points on serve in a penultimate game that lasted more than 11 minutes. Williams kept her cool, though, wasting one match point on her serve before closing with an ace to reach her 23rd major final. Williams was at her best after dropping her opening service game, finishing the match with just one double-fault, firing 13 aces and defending when she needed to defend.

Keys, who beat fourth-seeded and Wimbledon champion Petra Kvitova in the third round and Venus Williams in the quarterfinals, had control until she was broken in the sixth game.

She held in the 12th game, closing with an ace to force a tiebreaker, but quickly fell behind 4-1 with Serena firing two aces. She saved two set points with aces but had no chance of extending the tiebreaker when Williams hit another unreturnable serve, and started jumping for joy.

Williams broke early in the second set and raced to a 5-1 lead before Keys held, denying victory for one more game the woman who inspired her to take up tennis.

Top-ranked Williams hasn’t been in peak form in Australia, starting with a luckluster hit-out at the Hopman Cup, but has found a way to reach her first final at Melbourne Park since 2010.

“I was so off. I felt like I wasn’t moving well. I just wasn’t feeling great on the court,” she said. “It’s been so long since I’ve even been in a final here. I was kind of like, `Oh, let me just try.’ My theory now is to relax and play the match as best as I can.”’

Sharapova, who beat No. 10-seeded Ekaterina Makarova 6-3, 6-2 in an all-Russian semifinal earlier Thursday, has lost her last 15 matches against Williams.