The pair, who finished 14th at Beijing 2008 and missed the final by two places, advanced in ninth with their first aim to improve on their 10th from last year's World Championships in Shanghai.
The final will see the top 12 pairs compete again and repeat the same free program they performed on Monday, with the score added to their performance from the technical routine.
Russia’s 15-time world champion Natalia Ishchenko and 10-times world champion Svetlana Romashina are favourites for gold with China, Spain and Canada expected to contest the other podium positions.
Russia claim fourth Olympic synchro sweep
Great Britain’s hope of a top-eight finish – a pre Games target – will depend on overhauling Greek duo Evangelia Platanioti and Despoina Solomou.
“It was a good swim but there are still a few things to improve on and we need to get them fixed,” said Randall.
“Some of the technical aspects weren’t quite perfect, there were a few things that were a little bit off and hopefully we can correct those with a bit more work.
“Our reputation as a country is improving. We’d still like higher marks and there are countries that we think we can move ahead of in the future.”
Russia top Olympic synchro scoreboard, Brits sixth
Only way is up for GB synchro swimmers