Bar del Portro's close shave, it was otherwise another bad day for many of the leading players.
In a tournament that has already seen a host of upsets - including the second-round exit of women's top seed Agnieszka Radwanska on Tuesday - Del Potro also looked to be heading out after winning just one game in the opening set against Frenchman Mahut.
However, the Argentinian, playing in his first ATP Tour match of the 2014 season, managed to find some form just at the right time as he battled back to level the clash in the second set before going on to the earn a 1-6 6-3 6-4 victory.
"To be my first match after two months it was okay," said Del Potro on www.atpworldtour.com.
"The court and the balls are really fast and it's tough to play long rallies. And also Mahut serves really well, and he played a lot of slices and volleys.
"It's tough to feel the ball on the baseline. In the end I broke his serve in the third set, only once, and that was enough to close the match."
Del Potro's success did not herald a huge change in fortunes for the seeded players though, as four more of the top-rated challengers tumbled out on Wednesday.
Second seed Jerzy Janowicz was brushed aside in less than an hour by Ukraine's world number 55 Alexandr Dolgopolov, who went through 6-2 6-2, while number three Andreas Seppi was similarly despatched as Marinko Matosevic recorded a 6-3 6-4 win.
Julien Benneteau and Marin Cilic, seeded six and seven respectively, were also beaten.
Sergiy Stakhovsky accounted for Benneteau 6-3 6-2 while Denis Istomin was Cilic's conqueror with a 6-3 6-4 triumph.
Fourth seed Dmitry Tursunov, the 2008 Sydney champion, was also at risk of an early exit on Wednesday as well but he recovered from a set down to beat Lukas Rosol 3-6 6-3 6-3 and seal his berth in the last eight.
Other men's winners were home favourite and defending champion Bernard Tomic, who beat Blaz Kavcic 6-3 4-6 6-4, and Radek Stepanek, who saw off Albert Ramos 6-2 7-6 (7/5) to set up a showdown with Del Potro.
In the women's event, second seed Petra Kvitova secured her spot in the semi-finals with a 7-6 (7/4) 6-2 win over Czech compatriot Lucie Safarova but another ranked player bid farewell to the event as Sara Errani was defeated.
The Italian, the tournament's third seed, was beaten 7-6 (7/2) 6-3 by Bulgarian qualifier Tsvetana Pironkova, who reached the Wimbledon semi-finals in 2010.
Pironkova next faces Kvitova, while the other semi-final will pit fifth seed Angelique Kerber against Madison Keys.
Germany's Kerber defeated Spain's Carla Suarez-Navarro 6-2 6-4 while Keys progressed past Bethanie Mattek-Sands when her fellow American retired when 3-2 down in the first set.