Defensive frailties may still nag, but at least the vim and verve have returned to Liverpool's approach. More daunting opponents than Levski Sofia await in this afternoon's draw in Geneva. But a sense that Houllier has found respite from the maelstrom is swelling.
The Frenchman punched the air as the travelling partisans serenaded him at the end. This riotous victory was a timely antidote to the poison of the anonymous death threat being investigated by Merseyside Police.
"Scoring four goals away from home is a great achievement, a great performance," Houllier said. This was also a timely display.
Given the deplorable circumstances that scarred the build-up, neither Houllier nor his players could have been particularly perturbed by the hostile reception afforded them here. "Scouse bastards," spat one banner. The monkey chants directed at the substitutes Emile Heskey and Djimi Traoré in the warm-up were harder to ignore, but Liverpool soon had reason to taunt.
Within 11 minutes this tie was effectively settled and Levski's attempt to whip up a storm horribly undermined. An error helped breach the Bulgarians, Ilian Stoyanov's back-pass dribbling short of Dimitar Ivankov with Steven Gerrard bursting on to the loose ball. The England midfielder rounded the prone goalkeeper and, though a heavy touch offered Levski momentary hope of a reprieve, Gerrard's left-foot finish from close to the byline squeezed home.
Houllier's mood improved further four minutes later when Harry Kewell freed Michael Owen. The striker had scored only twice in 12 games since returning from injury, but timed his run superbly, veered into the penalty area and curled his 22nd European goal deliciously over Ivankov.
"I said he would score and that was a very important goal," said his manager with a smile.
Owen, tearing on to Bruno Cheyrou's excellent cross, might have added a second before half-time but will still look back on his performance with some satisfaction.
"It will help him," Houllier said. "He had an outstanding game, working extremely hard for the team on his own up front. His work-rate was phenomenal - he wasn't only a star player, but a team player."
There were team deficiencies, too. If the start had suggested a stroll, Levski's spirited fightback was a painful reminder that little has come easy to Liverpool this troubled season. Steve Finnan's form has dipped and his miscontrol was punished by Georgi Ivanov, sliding a shot across Chris Kirkland and into the corner. If that appeared to be a mere consolation, Sasha Simonovic's magnificent second - exploiting Stéphane Henchoz's slip - offered authentic hope.
Had Liverpool been gripped in a genuine crisis of confidence they might have capitulated. As it was, and with their two-goal advantage from the first leg still effectively unthreatened, they mustered an immediate riposte. Gerrard's corner, whipped into the far post, was headed emphatically in by Dietmar Hamann on the stroke of half-time.
After Kewell and Danny Murphy had threatened a fourth, it was left to Sami Hyypia, nodding the captain's cross powerfully down and in to celebrate his 250th appearance for the club, to add the second-half polish the visitors' overall display deserved.
"This was a good game and you need two good sides to make that possible," added Houllier.
Testing times lie ahead in this competition but, for once this term, Liverpool can look ahead with some optimism.