The 24-year-old was heading out when she fell a break behind to the powerful Keys in the second set, having squandered four set points in the opener, but she battled back and took ruthless advantage as Keys appeared to suffer a leg injury.
She will play Australian Open champion Angelique Kerber in the last eight.
Keys struck 32 winners to Halep's 13 and blasted down serves champion Serena Williams would be proud of, but racked up 48 unforced errors as the wily Halep weathered the storm.
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"Unbelievable (power)," Halep said of her opponent. "It was tough to return some balls. But I have strong legs, and I stay there low. I returned well. That's why I could win.
"The most important thing was that I stayed there, I kept my concentration till the end and I was fighting."
The first eight games were full of high-quality baseline tennis with no hint of a break point.
A strange passage of play followed during which both players went off the boil in equal measure.
Halep broke first when Keys failed to kill a volley and she scampered to her right to scoop the ball inadvertently over the 21-year-old American's head.
But she let her opponent off the hook, double-faulting on two of the four set points that came her way when she served at 5-4 in the opening set. Another she wasted with a rash forehand while Keys saved the other with a sizzling backhand return.
Keys' forehand then misfired as she was broken to love, but Halep again faltered at 6-5 as the American flashed a forehand winner past her, one of 16 in the match, to force a tiebreak.
Ninth seed Keys, the youngest player to reach the fourth round this year, surged ahead in the breaker and claimed it 7-5 with another crunching forehand winner into an open court.
When Halep double-faulted and then sent a backhand long to drop serve at the start of the second set and Keys held with a huge ace to lead 2-0 the end looked nigh.
But Halep, whose semi-final appearance two years ago disguises an ordinary Wimbledon record, is made of sterner stuff and worked her way back, breaking back in the fourth game as the errors returned to the Keys game.
Keys netted a forehand to hand the second set to a resurgent Halep and the decider became an ordeal for the American as she looked in discomfort and close to tears with a leg injury.
Surprisingly Keys, playing some shots off one leg, did not call for the trainer and Halep calmly moved 5-3 ahead, sealing victory when Keys belted a forehand out.
(Editing by Ken Ferris)
