Archive classics like Morecambe and Wise and Dad's Army helped Radio 4's sister station achieve record listeners of 2.17 million a week - an increase of half a million on the last quarter.
6 Music maintained its record audience with 2.06 million listeners.
Radio 2 is the most popular UK station with 15.09 million tuning in weekly.
BBC Radio 1 shed more than 700,000 listeners with 9.7 million, down from 10.43 million last quarter. The station said more than half a million of these were older.
"Since Radio 1 has been completely focused on younger audiences - and the most common age of a Radio 1 listener is 21 - it was highly likely some older listeners would move on, like the half a million over-30s that left us this quarter," said Radio 1 controller, Ben Cooper.
Radio 4 Extra airs comedy and drama from the BBC archive alongside new speech programmes like TED Radio Hour, Comedy Club and Newsjack.
Its recent successes include the decision to broadcast hit US podcast Serial at the end of last year.
"Radio 4 Extra was once a hidden gem in the BBC Radio portfolio," said director of BBC Radio Helen Boaden.
"These figures show the power of the BBC audio archive. Radio 4 Extra was created to make better use of Radio 4's incredible back catalogue and today's statistics show that brilliantly-made, high quality comedy and drama is timeless."
When the previous quarter's figures were revealed in February, BBC 6 Music became the first digital-only station to ever reach more than two million listeners.
Home to presenters such as Lauren Laverne, Steve Lamacq and Iggy Pop, it has almost tripled in popularity since a campaign to save it from closure in 2010.
Listeners for this quarter - between 5 January and 5 April 2015 - showed 2.06 million people tuning in each week, down slightly from 2.08 million last quarter and up from 1.93 million a year ago.
The Chris Evans Breakfast Show on Radio 2 is still the UK's most popular programme in the mornings with 9.46 million listeners tuning in every week, compared to 9.6 million last quarter and a record 9.83 million this time last year.
The Today Programme on Radio 4 recorded exactly the same amount of listeners as a year ago with 7.06 million per week - back up from last quarter's results of 6.77 million - while Radio 4 averaged 10.89 million listeners a week, a 12.8% share of the audience.
Radio 1's breakfast offering with Nick Grimshaw dropped from 5.91 million to 5.5 million listeners a week - with nearly 90% of those down to older listeners going elsewhere.
"I'm pleased that Grimmy is doing what I've asked of him by keeping his young audience happy and scaring off the over-30s," added controller Cooper.
Radio 2's total share of listening increased from 17.8% last quarter to 18.1%, despite the number of weekly listeners dropping from 15.28 million to 15.09 million.
Radio 3 reached an audience of 2.08 million between January and April - back up from 2.03 million last quarter.
The popularity of the cricket World Cup helped BBC 5 live Sports Extra reach its second highest figures yet with 1.32 million listeners, almost doubling last quarter's figures with an increase of 657,000.
Things improved for BBC Radio 5 live, with listeners increasing by more than 100,000 from 5.61 million to 5.76 million - after the station suffered a slump in the last few quarters.
Three of its most popular daytime presenters - Victoria Derbyshire, Richard Bacon and Shelagh Fogarty - left the station in September last year.
Digital stations Radio 1Xtra and Asian Network both suffered a drop in weekly listeners - with 839,000 tuning into 1Xtra (down from 1.11 million last quarter) and 562,000 listening to Asian Network, compared to 619,000 last quarter.
Local radio services from the BBC currently reach 8.82 million listeners a week, which is down on 8.98 million last quarter and 9.26 million the same time last year.
The BBC World Service reaches 1.35 million listeners a week in the UK alone, while the newly announced figures from the BBC show globally its radio stations have a weekly audience of 133 million people.
In the commercial radio sector, figures show Magic Radio has shown year-on-year growth of 29%, with a reach of 3.6 million.
Richard Dunmall, group managing director of Bauer Advertising, said: "This set of Rajar results reinforces the success of our radio strategy. The fact that we have increased our share in commercial radio shows our ability to produce strong brands and engage with valuable audiences across the UK."
BBC Radio 4 Extra has overtaken BBC 6 Music to become the UK's biggest digital-only station, according to the latest audience figures from Rajar.