Azarenka, playing her first grand slam since giving birth, had plenty of chances in the early stages of the opening set having broken twice.
Halep fought back on each occasion, though, and her level continued to increase as she ultimately coasted to a 7-6 (7-3) 6-2 victory, aided by numerous unforced errors from a frustrated Azarenka, on Court Two.
The Romanian faces Great Britain’s Johanna Konta (6) in the last eight and will secure the number-one ranking by beating the home-crowd favourite.
Halep toiled in her first service game and when she sent the ball sailing long Azarenka held a 2-0 lead, only for the Belarusian to hand the break straight back.
It was a case of deja vu when a perfectly executed drop-shot saw Azarenka break again, but a couple of poor errors into the net left the match on serve once more.
Azarenka’s body language slumped in the ensuing tie-break as Halep took command and the Romanian quickly seized the initiative.
Having failed to capitalise on her chances, the match began to unravel for Azarenka, and the error count continued to rise en route to gifting Halep a break for a 2-0 lead.
Halep was now completely dominant all over the court and Azarenka’s frustration boiled over as she received a code violation for throwing her racket at the turf.
Some nimble footwork to chase down an Azarenka drop-shot left Halep a double-break in front at the end of a lengthy game four.
There was a slight blip when serving for the set at 5-1 as Azarenka earned a break back, but it only delayed what had long been an inevitable Halep win as once again the former world number one contrived to cough up cheap points on serve and, with it, the match.
STATISTICAL BREAKDOWNHalep [2] bt Azarenka 7-6 (7-3) 6-2
WINNERS/UNFORCED ERRORSHalep - 19/11Azarenka - 21/32
ACES/DOUBLE FAULTSHalep - 1/3Azarenka - 1/2
BREAK POINTS WONHalep - 5/9Azarenka - 3/6
FIRST SERVE PERCENTAGEHalep - 68Azarenka - 65
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVEHalep - 63/57Azarenka - 53/50
TOTAL POINTSHalep - 76Azarenka - 64
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