Having gone into the show jumping in fourth, the Lithuanian produced an accomplished ride, knocking down just once fence to pick up 20 penalty points.
Asadauskaite starts the combined at the same time as Brazil’s Yane Marques, who picked up just 48 penalty points despite some less than perfect approaches to some of the fences.
Amelie Caze of France will start the combined two seconds behind the leaders after knocking down two fences in the show jumping.
Britain’s Samantha Murray will really fancy her medals chances, starting in fourth with an eight second handicap. The tough course at Greenwich Park will suit this strong runner. Murray had a reasonable ride, knocking down two fences but a few time penalties meant she picked up a total of 80 penalty points.
Adrienn Toth of Hungary went into the ride in first place, but five fences down cost her 25 seconds, so she will now begin the combined event nine seconds after the first two.
The top 11 athletes begin within 30 seconds of each other so the medal race is wide open if any of the leaders falter in the laser shooting.
Defending Olympic champion, Lena Schoneborn of Germany, had a poor ride and has probably left herself too much to do in the combined event. She starts the combined in 21st places, almost a minute behind the leaders.