The native of Humboldt, Sask., has 3,810 points to trail leader Ganna Melnichenko of Ukraine by just 102 points. She's only 26 points behind American Sharon Day, who is third.
Briesen was second after the first two events — 100-metre hurdles and high jump. She won the 100 with a time of 13.17 second and was sixth in the high jump with a leap of 1.83 metres.
Briesen fell to fourth overall after registering 732 points with a 13.07-metre effort in the shot put but accumulated 963 points after finishing the 200 in 24.18 seconds.
Dafne Schippers of the Netherlands is second overall with 3,837 points.
The final three events — long jump, javelin and 800 — are scheduled for Tuesday. The two-day event is considered wide open since Olympic champion Jessica Ennis-Hill and defending champion Tatyana Chernova are both out injured.
Theisen's husband Ashton Eaton, a gold medallist for the U.S. in the decathlon, was in the stands watching his wife. The two were married in July.
Canadians Matt Hughes and Alex Genest advanced to the men's 3,000-metre steeplechase.
Meanwhile, the U.S.-Jamaica sprint rivalry is turning into a rout. Shelly-Ann Fraser-Pryce rubbed it in Monday with a winning margin of Bolt-esque proportions in the women's 100 metres.
Her hot-pink coloured hair slashing in the air behind her, Fraser-Pryce flashed to an early lead and kept on building it before crossing in a world leading 10.71 seconds.
She had time to clench her fist as she crossed the line with silver medallist Murielle Ahoure of the Ivory Coast crossed a massive .22 behind.
The first American, defending champion Carmelita Jeter, took bronze in 10.94.
Like Usain Bolt, she now has two Olympic and two world titles in the 100. And in Moscow she gave Jamaica a 2-0 lead over the Americans in the sprint duel, showing the Caribbean island produces the fastest runners on the planet.
The United States got its part of the glory, too, when David Oliver led a 1-2 finish in the 110 hurdles.
It would have been an American sweep had defending champion Jason Richardson not stumbled near the end.
In the women's 400, Christine Ohuruogu set a British record to regain the world title she first won in 2007, dipping at the line to cap a great comeback and beat defending champion Amantle Montsho of Botswana by .004 seconds.
"When I finished I didn't know if I'd won it, I didn't want to get over-excited until my name came up," Ohuruogu said. "I heard everyone screaming and I looked up and I'm just so happy."
Through three days of competition, the United States leads the medals standings with three gold and six overall. Germany is second with four medals overall after Raphael Holzdeppe upset Olympic champion Renaud Lavillenie of France on a countback to win the pole vault.
In the shot put, Valerie Adams became the first woman to win four straight individual world titles.