Robert Baloucoune's hat-trick saw Ulster take a big step towards the Champions Cup quarter-finals as they claimed an away win over 14-man defending champions Toulouse.
The hosts played 70 minutes a man short after Juan Cruz Mallia's red card.
Baloucoune crossed once before the break and twice after with Andy Warwick also going over as Toulouse tired.
However, Romain Ntamack's late score means Toulouse are only chasing a six-point deficit in the second leg.
In a rousing finish the hosts even threatened to pull an unlikely win out of the bag having been staring at a 13-point defeat with just a minute left on the clock.
Ulster will now bring their advantage back to Belfast for the second leg next Saturday, with the winners of the tie set to face either Munster or Exeter Chiefs in the quarter-final.
With the return fixture in mind, Ulster knew a win in the first leg was less important than keeping the scoreline tight against a side that blew them away when they last met in Toulouse - in the rearranged 2019-20 quarter-final.
Mallia's dismissal after 10 minutes for taking out Ben Moxham in the air was a major early boost for the visitors having fallen behind when Meafou battered through their defensive line from close range.
Quick hands saw Baloucoune finish in the corner just three minutes after the red card as a shell-shocked Toulouse saw their early momentum shattered.
However the five-time champions, who have struggled for form domestically this season, gritted their teeth and went about disrupting Ulster's flow with ferocious work at the ruck that routinely succeeded in reclaiming possession.
After Ramos kicked the hosts back in front, the full-back was on hand to bring down Baloucoune with the Ulster wing poised to score what would have been the try of the tournament so far having slalomed past multiple defenders after collecting the ball on halfway.
Ulster enjoyed plenty of chances and put several penalties into the corner as they put faith in the maul that has served them so well in recent seasons.
However against a stubborn Toulouse pack they were unable to make ground, with Rob Herring twice breaking off and becoming isolated allowing the hosts an opportunity to execute some sublime counter-rucking and clear the danger.
Having for the most part struggled to capitalise on their numerical advantage throughout the first half Ulster banked on more space opening up after the break.
Five minutes into the second half the province moved the ball right for Stuart McCloskey to charge through a gap and hold his pass long enough to draw the last defender and send Baloucoune in for the easiest of finishes.
With their backs against the wall Toulouse refused to deviate from their expansive gameplan, and looked to have scored a sensational try having ran the ball from deep inside their own 22 up to the line where Matthis Lebel touched down, only for video replays to show a knock-on from Antoine Dupont that saw the try chalked off.
Defensively their effort was relentless, but Ulster showed patience and poise to hold on to the ball long enough for Warwick to dive over the line after his side had been repelled for multiple phases.
Baloucoune's hat-trick try - an intercept from Dupont's pass - looked to seal a memorable win for Ulster, but the hosts rallied late with Ntamack finding space to claim a potentially crucial late try in the final minute.
Toulouse: Ramos; Mallia, Holmes, Ahki, Lebel; Ntamack, Dupont; Netil, Mauvaka, Aldegheri; RO Arnold, Meafou; Elstadt, Flament, Cros.
Replacements: Cramont, Baille, Faumuina, RI Arnold, Jelonch, Placines, Page Relo, Guitoune.
Ulster: Lowry; Baloucoune, Hume, McCloskey, Moxham; Burns, Cooney; O'Sullivan, Herring, Moore; A O'Connor, I Henderson; Marcus Rea, Timoney, Vermeulen.
Replacements: Roberts, Warwick, O'Toole, Treadwell, Murphy, Doak, Marshall, Lyttle.