Her husband, Andrejus Zadneprovskis, won silver in modern pentathlon in 2004 and bronze four years later. At the London Games on Sunday, Asadauskaite added the one medal that couple was still lacking.
"He really helps me out in our daily life," Asadauskaite said. "With our child and also with my training."
Asadauskaite stopped her run at the final event just before the finish line. Then she crossed it very slowly, as if she wanted the actual moment of winning the missing medal as long as possible.
She threw her arms in the air and finished her race, 3.5 seconds ahead of her rivals.
"I am immensely excited," she said. "I had a great deal of support from the people of Lithuania. It is only a small country so this means the world to them. I felt very excited and emotional when the crowd cheered for me."
Asadauskaite and Yane Marques of Brazil were tied for the lead going into the combined event of running and shooting.
Marques shot five out of five to take a 10-second lead after the first round of shooting, but Asadauskaite ran the one-kilometre lap faster and overtook the Brazilian just before the second shooting round and stayed ahead of the field.
Marques then even lost silver as she was overtaken by Britain's Samantha Murray, who was loudly cheered by a home crowd of 22,000.
"I can't put it into words right now. It's surreal," Murray said. "No way was I going to let a medal get away. I was running for a medal — I was running for silver. I will never forget this day."
Despite going into the lead in the final event before finishing third, Marques said she was "very happy. I have been training hard for four years and now the job is done. I am very tired but very happy."
Margaux Isaksen took fourth for the best Olympic result by an American athlete in the modern pentathlon.
Isaksen, who recovered from a virus infection earlier this year, said her result was "pretty bittersweet."
"I wasn't able to train for the first four months of the year and running is my best event," she said. "I was so close to a medal. You can also say, what if? But my swimming was a few seconds slower and my running was significantly slower than what I hoped for."
Melanie McCann of Mount Carmel, Ont., was 11th while Toronto's Donna Vakalis was 29th.
Adrienn Toth of Hungary, who led the event after the first two disciplines, knocked down five rails and earned just 1,100 points at riding, and ultimately finished the competition in 20th place.
World champion and home crowd favourite Mhairi Spence had four mistakes and got a time penalty for exceeding the 75-second limit. The British athlete was also unlucky in the final event as there was a technical problem with her laser gun.
"After 50 seconds, an official told me I could go on," said Spence, who was fighting her tears after finishing 21st. "It really didn't get going today ... It's great we have a medal though, I am very pleased for (Murray)."
Defending champion Lena Schoneborn's horse Zidane refused the first obstacle, but the German had a solid ride afterward and knocked down just two fences. However, she dropped to 21st in the standings and had no change left to defend her title.
Three athletes fell off their horse at misjudged jumps. In a spectacular move, Tamara Vega of Mexico managed to complete a triple jump while hanging around the horse's neck after sliding off the saddle.
Iryna Khokhlova of Ukraine, riding Liberty XII, became the only athlete to complete the course without mistakes and within the time limit, scoring the maximum of 1,200 points for the discipline.
Earlier, Sarolta Kovacs of Hungary set an Olympic swimming record for women's modern pentathlon in the 200-meter freestyle.
Kovacs finished in two minutes 8.11 seconds, shaving 0.75 off of the four-year-old best mark set by Sheila Taormina of the United States at the Beijing Games.
Murray came second in 2:08.20 and also beat Taormina's time.
Schoneborn, who was only 11th after her preferred fencing discipline, lost further ground as she posted the 22nd time in the pool.
In the first event, Elena Rublevska of Latvia won 25 out of 35 fencing bouts to take an early lead in the competition.
A 2004 silver medallist , Rublevska looked set for an Olympic record when she went 20-5, but she lost five of her next 10 duels to fall three wins short of Schoneborn's games mark from the 2008 Beijing Games.
Rublevska, the only athlete having competed in all four Olympics since women's modern pentathlon was added to the program in Sydney in 2000, took eighth in the end.