The world number one dropped a set for the first time in the WTA Premier hard-court event on Thursday, before eventually prevailing 6-1 1-6 6-2.
The defending champion romped to the opening set with breaks in games two and six, but Safarova stormed back in the second set, reeling off five successive games from 1-1 to force a decider.
A double break saw Williams serving for the match at 5-1 and although Safarova clawed one game back, the top seed responded immediately to close out the match.
World number two Halep, who defeated 2011 runner-up Andrea Petkovic 7-6 (7-4) 5-7 7-6 (7-1), will play no further part in the tournament after a hip injury ended her participation.
Halep's injury means Ana Ivanovic progresses straight through to the semi-finals.
Ivanovic had earlier defeated Sabine Lisicki 6-3 7-5, while Williams' elder sister Venus was unable to join her sibling in the last eight, as she was forced to pull out of her clash with third seed Petra Kvitova due to a viral illness.
Kvitova will now face Roberta Vinci in the quarter-finals, after the Italian saw off Ekaterina Makarova 6-1 0-6 7-5.
Serena Williams' opponent in the last eight will be Australian Samantha Stosur, who had little trouble in seeing off Alize Cornet 6-4 6-2.
Elsewhere, Svetlana Kuznetsova came from a set down to overcome Angelique Kerber 2-6 6-4 6-3, booking a quarter-final clash with fourth seed Maria Sharapova.