Romania's Halep, 23, beat Belarusian Victoria Azarenka 6-3 4-6 6-4 in a rain-interrupted match in New York.
Pennetta, 33, capitalised on two-time Wimbledon champion Petra Kvitova's inconsistency to win 4-6 6-4 6-2 and reach her second US Open semi-final.
Roberta Vinci and Serena Williams will contest Thursday's other semi-final.
With both Pennetta and her compatriot Vinci in the last eight, two Italian women have made the last four of the same Grand Slam tournament for the first time in the Open era.
Construction of a retractable roof is due to be completed over the top of Arthur Ashe Arena in time for the 2016 tournament
Former world number one Azarenka, who spent 51 weeks as world number one earlier in her career, is climbing back up the rankings after a series of injuries over the past two seasons.
Halep looked in danger as her 26-year-old opponent came into the third set with momentum after winning the second in impressive style.
