The world number one found it tough going during the second set but when it came to the tiebreak, she produced her full array of shots to outwit Haddad Maia and set up a Saturday showdown with unseeded Czech Karolina Muchova (26).
Swiatek, who lifted the Suzanne Lenglen Cup last year and in 2020, will retain top spot in the WTA rankings after world number two Aryna Sabalenka (25) of Belarus was knocked out earlier.
As fans waved a Polish 'Poland Garros' flag in stands that were half empty when the match started, Swiatek showed rare signs of frustrations but managed to hold it together when it mattered to prevail as the clock hit the 9pm mark.
The 14th-seeded Haddad Maia, whose career has been hampered by multiple injuries and a 10-month doping ban in 2019-20, had played four consecutive three-set matches to fight her way to the semi-finals but she finally met her match in Swiatek.
Swiatek's previous matches had lasted only a little over an hour each, while Haddad Maia had spent nearly 13 hours on court.
Sent scurrying right, left and centre by Swiatek, the Brazilian relied on her power to try and stop the top seed from running away with the match.
Haddad Maia broke to love in the opening game on Court Philippe Chatrier, where most of the ticket holders for a sold-out day had decided to skip the start of what turned out to be an entertaining encounter.
It did not take Swiatek long to find her groove as she stole her opponent's serve to level for 1-1. She got a second break for 4-2 when Haddad Maia netted a drop shot attempt and sealed the set with another break of serve.
It seemed that Swiatek would stroll through the second set, but Haddad Maier had other ideas.
The Brazilian picked herself up and finally gave Swiatek a run for her money, setting up two break points at 4-4 with a stunning forehand down the line.
With two big first serves, Swiatek saved them and staved off another one before holding, forcing Haddad Maia to serve to stay in the match.
The Brazilian held on to stretch the match into the tiebreak but she wasted a set point when she buried an easy backhand into the net.
Swiatek earned her first match point with a jaw-dropping crosscourt backhand winner, which her opponent saved with a stunning forehand down the line. The Pole had a second opportunity to close out the match at 8-7 and converted it at the net before throwing her fist in into the air in relief.
