The 25-year-old is the favourite for gold and has 2,111 points, 27 clear of second-placed Canadian Nina Schultz.
Johnson-Thompson, who won the World Indoor pentathlon title last month, was fifth after the opening 100m hurdles but moved top with a joint-first finish in the high jump.
England’s Niamh Emerson is in fifth and Scotland’s Holly McArthur and Katherine O’Connor are tied for ninth.
Johnson-Thompson finished fourth in her 100m hurdles heat in a time of 13.54 seconds.
She reached a height of 1.87m in the high jump, which was enough to move into the lead, despite being 0.11m below her personal best.
The shot put and 200m take place later on Thursday with the long jump, javelin and 800m on Friday.
Elsewhere at the Cararra Stadium, England’s Tiffany Porter and Alicia Barrett qualified for the 100m hurdles final.
England’s Alexandra Bell ran a personal best to reach the women’s 800m final as the second-fastest qualifier behind South Africa’s Olympic champion Caster Semanya but Scotland’s 2014 silver medallist Lynsey Sharp missed out.
England’s Sophie McKinna, Rachel Wallader and Amelia Strickler secured a place in the women’s shot put final and England’s Nathan Douglas progressed to the men’s triple jump final.>