Unseeded American Pegula claimed the opening set in hot conditions in Melbourne, but 22nd seed Brady fought back to reign supreme.
Brady will now contest a second major semi, having also featured in the US Open's final four last year, with Ash Barty's quarter-final conqueror Karolina Muchova next up at Melbourne Park.
American Brady had only conceded 17 games en route to the quarters - the fewest of any player in the draw, while she only dropped serve twice during that run.
Brady was upstaged by compatriot and good friend Pegula in the opening set in the first all-American quarter-final at the Australian Open since Madison Keys defeated Venus Williams in 2015.
Pegula – the daughter of the owners of NFL franchise the Buffalo Bills and NHL team the Buffalo Sabres – converted both of her break-point chances and hit six winners, but it was her unforced error count of seven that was decisive, with Brady reaching 17 in 33 minutes.
The pair were meeting for the first time since Pegula prevailed at the 2020 Western & Southern Open and after digging herself out of a 15-40 hole in the opening game of the second set, Brady held serve before breaking herself for a 2-0 lead.
Having found herself under early pressure, Brady – reducing her unforced errors to just six – did not look back as she levelled the match and forced a deciding set.
Brady and Pegula traded breaks at the start of the third set, but the former broke again in the fourth game for a 3-1 lead and never looked back en route to the semis.
Data Slam: Brady stays flawless against compatriots
The only other time Brady met an American at a slam was last year, when she defeated CiCi Bellis during her semi-final run. Brady added Pegula to that list to make it two from two.
Brady – 22/29
Pegula – 15/32
Brady – 7/5
Pegula – 0/3
BREAK POINTS WON
Brady – 7/10
Pegula – 4/10