The 34-year-old American was broken just once as she claimed a 6-4, 6-3 win over her Romanian opponent and continued her quest for a record third women’s singles title at the event.

Victory extended Williams’ superior head-to-head record against Halep to 7-1 and means she will now go on to face Poland’s Agnieszka Radwańska in the last four on Friday (March 18).

Radwańska defeated Czech Republic’s Petra Kvitová 6-2, 7-6, thus ensuring that she will reclaim the world number two ranking when the new list is released on Monday (March 21).

"[Radwańska] knows how to play in big stadiums and big matches, big games," said the world number one Williams, who has yet to drop a set in this year’s tournament.

"Obviously she does everything so well, including running, and this is a good surface for her because it's a slow surface.

"I think I expect there will be a lot of long rallies."

In the men’s draw, Rafael Nadal survived a major scare against 18-year-old German Alexander Zverev before prevailing 6-7(8), 6-0, 7-5 in two hours and 34 minutes.

The fourth-seed faced a match point, but after Zverev missed an easy forehand volley, Nadal took control.

The 29-year-old Spaniard won 15 of the last 16 points to secure a place in the quarter-finals, where he goes up against Japan’s Kei Nishikori.

Nishikori edged the United States’ John Isner 1-6, 7-6(2), 7-6(5) to reach the last eight in Indian Wells for the first time.

The winner of Nadal’s clash with Nishikori could meet world number one Novak Djokovic in the next round after the Serb overcame Spain's Feliciano Lopez 6-3, 6-3 to set up a quarter-final with France’s Jo-Wilfried Tsonga.

Tsonga dismissed in-form Austrian Dominic Thiem 6-3, 6-2 in the final match of the day.