The Liverpudlian is second on 3,932 points, 40 behind leader and reigning champion Brianne Theisen-Eaton.
Johnson-Thompson has said her main aim this weekend is to get the 6,200 points needed for Rio.
She needs 2,268 points on Sunday in the three remaining events.
The 23-year-old began the day equalling her personal best of 13.37 seconds in the 100m hurdles and followed it up by clearing 1.92m in the high jump, a personal best outdoors.
After two events, Johnson-Thompson was in the overall lead but slipped to sixth following a disappointing 11.55m in the shot put - the worst mark in the field and 1.59m below the personal best she set earlier in the season.
She made amends for that poor display with a personal best 22.79 secs in the 200m, which pulled her closer to Canada's world silver medallist Theisen-Eaton.
Johnson-Thompson will start with the long jump on Sunday, the event which ruined her chances of gold at last year's World Championships following her failure to record a legal jump.
She said: "I'm sure I'll be nervous again in the long jump. I really want to get a good jump in the first round.
"This is my first big competition especially after a knee operation last autumn so I just want 6,200 points and to be injury free and to be going home with my ticket for the Olympics."
The Briton has also said her experience in Beijing changed her, created a "new Kat" who is determined to bounce back and quash her demons.
Her performances on the opening day in Austria promised much not only for this competition but the summer ahead.
Although she has repeatedly said Olympic qualification rather than regaining the title she won in 2014 is her priority this weekend, she looks set to vie with favourite Theisen-Eaton for first place.
And despite a poor display in the shot, her weakest event, Johnson-Thompson will take heart that she achieved her best heptathlon score of 6682 points in Gotzis two years ago, when her total after the opening day was also 3923.
The long jump, javelin and 800m remain on Sunday but fellow Brit Morgan Lake - adrift of her personal bests in all four events on the first day - is likely to fall short of the total needed for Rio.
Lake - recording 14.43 secs in the 100m hurdles, 1.86m in the high jump, 13.18m in the shot put and 26.12 secs in the 200m - is 29th overall.
British decathletes John Lane (4159 points) and Ashley Bryant (4121 points) are ninth and 13th respectively at the halfway stage in Austria, with the pair needing 8100 points to be selected for the Olympics.
Britain's Katarina Johnson-Thompson is on course to qualify for this summer's Rio Olympics after setting three personal bests on the opening day of the Hypo meeting in Gotzis.