The 6-foot-5 Australian star hopes there is more to come.
Her latest milestone came Wednesday when she scored 18 points and surpassed the former U.S. standout while leading Australia to a 67-61 victory over Brazil.
Jackson had no idea she was in reach of Leslie's mark.
"I didn't know about that until a few minutes ago. I haven't even thought about it. I guess it means I'm old," Jackson said laughing. "It's a great honor, but we're really just trying to win games."
Jackson needed just 10 points entering the contest to pass her one-time American rival, who had 488 points while leading the U.S. to four consecutive gold medals from 1996-2008 - three coming at Jackson's expense.
The London Games are the fourth Olympics for the 31-year-old Australian star.
Jackson broke the record by hitting a free throw with 53 seconds left in the third quarter which gave Australia a 51-40 lead.
Brazil (0-3) couldn't get within four the rest of the way.
The Aussies were coming off a 74-70 overtime loss to France - their first defeat in the Olympics to a team other than the United States since the 1996 Atlanta Games.
"It was huge, we needed to get our confidence back," said Jackson, who has led Australia to silver medals in the last three Olympics. "We wanted to play well. Liz (Cambage) was great."
Australia struggled at the beginning and trailed 10-8 before Jackson keyed a 13-2 run by scoring five points. Her lay-in with 7:41 left in the second quarter made it 20-12. Australia extended the lead to 13 at the half.
Brazil rallied behind Karla Costa to come within 45-40, but Suzy Batkovic had five straight points to restore the double-digit lead. Jackson then hit one of two free throws to break Leslie's mark.
"In terms of women's basketball she's iconic in our country," Australia coach Carrie Graf said. "For a small country like ours she continues to help put the Opals on the map. I think it's fitting at this Olympics that as the flag bearer she gets the record."
Australia couldn't put away Brazil though, which rallied within four on Costa's 3-pointer with 16.3 seconds remaining. That's as close as the Brazilians would come as Jackson hit two free throws a second later to seal the win.
Cambage finished with 17 points for Australia.
Costa scored 22 points and Erika de Souza added 11 before fouling out to lead Brazil, which used to be a consistent medal contender, winning a silver in 1996 and bronze in 2000. The Brazilians finished fourth in 2004 and 11th in 2008 with the lone victory coming over Belarus.
Brazil spent months training together before the Olympics and have nothing to show for it so far.
"We all need to take a shower and try to think of what comes next," Costa said. "We finally played our best. We wanted to be first then we wanted to be second, then third and now we want to be fourth.
"As long as there's a chance we'll fight for that."
They could still qualify for the quarterfinals with victories in their final two games over Canada and Britain.