World number two Sharapova won an all-Russian contest against Ekaterina Makarova 6-3 6-2.

Williams, the top seed, converted her ninth match point to beat fellow American Madison Keys 7-6 (7-5) 6-2.

Britain’s Andy Murray takes on Czech Tomas Berdych in the first men’s semi-final at 08:30 GMT.

Williams, 33, capped a fine performance with a dramatic ending as she saw seven match points slip by at 5-1, before converting her ninth with an ace and a scream in the following game.

Keys, 19, matched Williams for power but not always control as the 18-time Grand Slam champion edged a tight match over one hour and 24 minutes.

The world number one, a five-time champion in Australia, recovered from 3-0 down to force a tie-break and clinched it with a big serve.

A fired-up Williams bounced up and down in delight at the baseline, and powered on with a break at the start of the second as she began to dominate the Keys second serve.

Williams flipped a brilliant forehand winner around the net post on her way to breaking again at 4-1 and eventually closed out after that gripping seventh game.

Sharapova, the 2008 champion, had earlier needed one hour and 27 minutes to beat 10th seed Makarova for the sixth time in six meetings.

The 27-year-old coped well on serve after saving two break points in a testing 10-minute opening service game, easing into a 4-1 lead.

Makarova, 26, hinted at a comeback when she broke for 4-3 but Sharapova responded immediately and served out the set after 48 minutes.

When she hammered away a backhand for the double break at 3-0 in the second, there was no way back for Makarova