Thanks to a round of 2-under 70, punctuated by a 40-foot eagle make on the 18th green, the 21-year-old will enter the final round one shot off the lead, tied for second with Dustin Johnson.
Describing the putt, du Toit said it "looked like I actually hit it a little too hard, but dead center and, you know, was pretty fired up about it."
"That's probably the biggest putt of my career, just atmosphere-wise. Unbelievable feeling."
The Arizona State Sun Devil is looking to become the first amateur to win on Tour since fellow Sun Devil Phil Mickelson in 1991. The British Columbia native is also looking to become the first Canadian to win his national open since Pat Fletcher in 1954.
Asked after the round if he can handle the pressure and take home the trophy, du Toit answered: "I have no idea. I've been surprising myself all week. You know, if I play good, solid golf, get a good night's sleep, do all the little things right, yeah, I like my chances."