The result saw Ulster go second in Pool 5 on nine points, three behind leaders Clermont, who picked up two bonus points.
Ulster edged Clermont 39-32 in a nine-try thriller as Munster and Glasgow also sent out European Champions Cup markers on Saturday.
The result saw Ulster go second in Pool 5 on nine points, three behind leaders Clermont, who picked up two bonus points despite the defeat.
There was more French heartbreak when last season's losing finalists Racing 92 went down to a 23-14 defeat by Glasgow.
Racing, featuring a glut of internationals including ex-All Black playmaker Dan Carter, currently sit last in Pool 1 with no points
Munster are atop the pool after handing Leicester a record European loss, running out 38-0 victors at their near-impregnable Thomond Park ground.
Racing took the lead against Glasgow through Juan Imhoff, but the Scottish side then took over through two tries from Alex Dunbar and Ali Price, with Finn Russell kicking 13 points before Carter pulled back a converted try near the death.
Munster's demolition of Leicester was thanks to tries from Simon Zebo, Jaco Taute (2) and a penalty try, New Zealander Tyler Bleyendaal hitting four penalties and three conversions.
A see-saw first-half in Ulster's home of Belfast was witness to two ambitious teams willing to run everything saw the lead change hands seven times.
Clermont's Fijian No 8 Peceli Yato opened the scoring, Ulster's Luke Marshall splitting the defence for a straight run-in and then Ian Henderson crossing after a Ruan Pienaar cross-kick as Ulster roared back.
But slick hands saw South African-born France full-back Scott Spedding go over before Paddy Jackson gathered his own grubber to hand the advantage back to the Irish province at the end of an enthralling first 40 minutes, 22-18.
A high-tempo start to the second period saw Marshall crash over for his second, All Black full-back Charles Piutau outpacing the defence after bluffing his way into space down the right wing to cross in the corner.
But Clermont hit back through England winger Nick Abendanon to keep the French side in the hunt. Skipper Damien Chouly then went over, Morgan Parra's conversion taking Clermont to within five points.
Ulster had New Zealand-born prop Rodney Ah You sin binned late-on for a high tackle, and the Irish province tried to run down the clock, with Pienaar at the helm. But with 20 seconds to play, they gifted Clermont a final chance, a knock-on in midfield ending French hopes.
Toulouse notched up a 36-6 bonus-point Pool 2 win away at Zebre, Hugo Bonneval (2), Gael Fickou, Joe Tekori and Yoann Huget all scoring for the visitors in a match which ended with 16 minutes to play because of thick fog.
The game had been a must-win for Toulouse, with Wasps and Connacht playing Sunday in the pool's other game.