After trailing 11-6 at half-time in Pool 4 at Ravenhill, Ulster fought back to leave the star-studded visitors with a losing bonus point after they had set all the early pace.
Ulster out-half Ian Humphreys scored all of Ulster's points, with his second-half try putting his side in front for the first time in the match, which he then converted to add to his earlier three penalties.
However, Humphreys was pipped to the man of the match award by flanker Stephen Ferris, who played an enormous role in weathering the Clermont storm and getting his side back into a game they had trailed in until the 68th minute.
As for Clermont, too many of their star names simply could not live with Ulster's pressure game and Morgan Parra lost his composure on several occasions, while their three place-kickers, Parra, David Skrela and Brock James, hardly covered themselves in glory.
The French side started the game at an ominous-looking pace and won back the kick-off after Pedrie Wannenburg lost possession to a Skrela kick that had huge height on it.
From there, Ulster were immediately on the back foot and, although Parra missed an early penalty, it was little surprise when Clermont scored the first points.
From a lineout they moved the ball to Aurelien Rougerie and the powerful France centre transferred the ball to Lee Byrne, who burst through Ulster's defensive line and fed winger Noa Nakaitaci, who had time and space to pick his spot over the line.
Parra was wide with the conversion but Clermont had made an early statement and Ulster needed to respond.
They did and with Ferris showing his power in lifting Parra off the ground and winning a turnover, Ulster were awarded a scrum and new signing John Afoa won a penalty off Darit Zirakashvili, which Humphreys crucially nailed.
However, Clermont managed to get the next points on the board when Tom Court was pinged at a ruck and this time Skrela put the ball between the sticks to make it 8-3 after 17 pulsating minutes.
Ulster again responded and a quick penalty from Paul Marshall again saw Ferris make hard yards and put his side into Clermont's 22, although from a good attacking platform Humphreys' pass was intercepted, and Rougerie's boot downfield led to a huge chase between flankers Chris Henry and Gerhard Vosloo which the Ulsterman won but led to a penalty against Vosloo for diving on his opposite number.
From this phase of the game, Skrela was then wide with a drop goal but with three minutes to go in the half he made sure with a penalty to put Clermont eight points in front.
But again Ulster came straight back and, after Andrew Trimble won the restart, Clermont conceded a penalty at a ruck and Humphreys, in the last act of the half, slotted the kick to make it 11-6 to the visitors at the turnaround.
Indeed Ulster had a chance to further eat into Clermont's lead when they won another penalty against the French side's scrum, only for Humphreys to miss the chance.
But he made no mistake in the 50th minute after a great drive from Henry and Dan Tuohy from a lineout, to leave Ulster trailing by just two points.
Clermont's replacement out-half James made a hash of a long-range penalty attempt for Clermont after 52 minutes, and the French were ultimately punished when, eight minutes after the hour, replacement full-back Adam D'Arcy took off on a run up the left wing and he linked with Humphreys who crossed the line.
It came out of nothing and, to rub further salt in Clermont's wounds, Humphreys nailed the touchline conversion to hand Ulster the lead for the first time in the game.
With five minutes to go, James was then wide with another penalty but Ulster kept up the pressure even after Ferris had limped off in the 76th minute.
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