Felipe Contepomi landed two penalties for Leinster with Ulster's Ian Humphreys and Clinton Schifcofske replying.
Adam Larkin replaced the injured Humphreys seconds before Biarritz scored their second try after 63 minutes.
BBC: SPORT | Rugby Union | European Club | Ulster 8-24 Biarritz
With seven minutes remaining, Humphreys finally broke his duck to kick Ireland 18-17 ahead.
The primary inventors of Ii-key hybrid tech are Dr Robert Humphreys and Dr Minzhen Xu.
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Humphreys missed the conversion but it could not take away from a magnificent Ulster performance.
Humphreys slotted over a penalty before Ferris stormed through for a converted 13th-minute try.
Man-of-the-match Humphreys missed his final conversion attempt - the only blemish in an outstanding display.
Pienaar, having missed two conversions, gave way to Humphreys who slotted an excellent touchline conversion.
King Williams College principal Martin Humphreys said it was a "very serious matter" and a pupil had been excluded.
"The great coaches out there are not available at the drop of a hat, " Humphreys said.
In the past year, Dr Humphreys's team has improved its silicon-based ones from 15% to 45%.
"It is disappointing it happens, and disappointing it happens with the same guy, " said Humphreys.
David Humphreys, Andrew Trimble, Tommy Bowe, Simon Best and his brother Rory are all on international duty.
Fly-half David Humphreys is a very senior international player and a very important member of O'Sullivan's side.
Humphreys landed four penalties and converted two of Ireland's five tries to become Ireland record points scorer.
But Humphreys' and Jones' kicking duel continued to the death as both sides failed to claim victory.
Humphreys responded with two failed long-range penalty attempts either side of a drop-goal effort that drifted wide.
Ireland fly-half David Humphreys and another World Cup prospect Jonathan Bell will both miss the Ravenhill game.
Humphreys is being rested after picking up a minor leg knock in Saturday's international win over Wales.
Mr Humphreys' family described him as a "fantastic son and brother" and praised hospital staff for their efforts.
With Humphreys retiring hurt, Ulster never regained their shape, though in truth their forward effort had already imploded.
BBC: Paul Steinmetz gave Ulster the perfect start at Ravenhill
Ulster fly-half David Humphreys, who kicked 17 points, singled out Ballymena young star Paddy Wallace for special praise.
Ian Humphreys took his tally to 20 points by converting Ian Whitten's try before Davies completed a double.
In 1992, Ms Humphreys was honoured with an Order of Australia for her work helping former child migrants.
The visitors led 13-3 at the break through Ian Humphreys' drop-goal, his try and another by Paddy Wallace.
Chris Humphreys, 24, from Handsworth in Sheffield was wounded at a property in Handsworth Grange Road on 5 May.
David Humphreys set up Tommy Bowe for Ulster's first try early in the second half but Augusto Petrilli replied.
Instead they fell further behind when following a break out from defence by Best, Humphreys landed his third penalty.
David Humphreys levelled to pass the 500-point mark in the Cup, but Biarritz surged clear after Petru Balan's try.
BBC: SPORT | Rugby Union | European Club | Ulster 8-24 Biarritz
With Humphreys adding his third conversion Ulster now led 21-3 and looked odds on to secure a bonus point.
BBC: Paul Steinmetz gave Ulster the perfect start at Ravenhill
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