With 37 horse-rider pairings still to go on Sunday - including the current world one and two - Klimke and German teammate Dirk Schrade held the top two spots in the standings, closely followed by British veteran Mary King in third.
But the contest will be far from over on Sunday, even if others overtake her.
The two-day dressage segment will be followed by eventing's signature cross-country competition on Monday and the jumping leg on Tuesday, when the team and individual victors will be crowned.
Germany is seen as the team to beat but Australia, New Zealand and the home team are also fielding strong riders.
"It's so wide open," said British team member Kristina Cook, who will ride on Sunday.
Klimke's father Reiner Klimke is one of Germany's most illustrious dressage riders and holds the record for the most equestrian Olympic medals: six golds and two bronzes.
Australia also enjoyed a strong day.
Andrew Hoy and mount Rutherglen were in fourth with Sam Griffiths - the second substitute dropped into an injury-hit Australian team ahead of the Games - in seventh and Christopher Burton in eighth.
Griffiths showed no sign of nerves in the arena, despite being capped just two days before Saturday's competition.
Since eventing horses are generalists and must excel in three very different disciplines, they do a less difficult test - or pre-set series of movements - than competitors in pure dressage.
Judges assess the freedom, regularity and forwardness of each horse's paces, along with its submission to the rider and the rider's position and skill, to determine a percentage score.
In eventing, these scores are converted into penalty points, which are added to penalties incurred in the ensuing two legs of the competition - cross-country with its huge solid fences and show jumping, where care is again the order of the day.
After Saturday's test, Klimke was on a low 39.30 penalty points, Schrade a hair's breadth behind on 39.80 and Mary King within reach at 40.90.
The score was a personal best at this level for King, who thrust a fist to the sky after finishing and rode waving out of the arena as the predominantly British crowd roared approval.
There were disappointments in the day as well - world number three Boyd Martin, first to ride, notched up 50.70 penalties to finish an unlucky 13th.
Asked how he felt about the score, U.S. Eventing Team coach Mark Phillips told reporters: "Boyd was pretty disappointed and I think everyone watching felt the same."
Martin said before his test that mount Otis Barbotiere, which he rescued from a stable fire last year, can be "a bit wobbly" but has improved recently.
Phillips will have more than his share of tension at these Games - daughter Zara Phillips from marriage to fellow former Olympic eventer Princess Anne is on the rival British team and rides her test Sunday morning.
Queen Elizabeth's granddaughter has already attracted feverish media attention since being picked for the team and with the Duke and Duchess of Cambridge and Prince Harry expected in the crowd, the cameras will be out in force.
Sunday's roster also includes a host of names to beat, including world number one William Fox-Pitt of Great Britain, number two Andrew Nicholson of New Zealand and compatriot and double gold medallist Mark Todd.
- Reiner Klimke