The Polish star, who won a fourth French Open and fifth Grand Slam title last month, was stunned 3-6, 6-1, 6-2 by the Russian-born Kazakh, who goes on to face the equally fiery Jelena Ostapenko for a quarter-final place.
"Feels great, I was just so focused on just playing fast and not giving her any time and that's pretty much it," said 29-year-old Putintseva after her win on Court One.
"I was thinking during the match that I had already beaten a world number one on grass so I think it was meant to be," she added, recalling her win over Naomi Osaka in Birmingham in 2019.
"This is crazy guys, it was great energy from all of you and I was trying to entertain you more and more with my shots and I was taking energy from you guys."
After winning the first set, it appeared business as usual for Swiatek, who went into Saturday's match with a 4-0 head-to-head record over the 35th ranked Putintseva.
However, the diminutive Putintseva stormed back in the second set on the back of breaks in the fourth and sixth games.
Putintseva held her nerve to cruise to a double break and a 4-0 lead in the decider.
Swiatek saved two match points but was defeated on the third when she buried a forehand return into the net.
The Pole, who has never got past the quarter-finals at Wimbledon, committed 38 unforced errors to Putintseva's 15. The Kazakh saved seven of eight break points.
It was only the fourth time in the Open era that the Wimbledon top seed had lost in the third round.
That fate befell Ana Ivanovic in 2008, Serena Williams in 2014, Simona Halep in 2018 and Swiatek, who was stunned by Alize Cornet at the same stage two years ago.
Putintseva, a three-time Grand Slam quarter-finalist, extended her grass-court streak this year to eight wins and no defeats after winning the Birmingham title last month.
