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The unrelenting Leinster machine, guided by former player Leo Cullen and ex-England coach Stuart Lancaster, suffocated the free-flowing, offloading game Toulouse have been employing to such success this season.
The loss was their first since September and brought to an end a 12-match undefeated run.
"We managed possession quite well in the first half. Toulouse had this big wall of defenders the whole time and our guys showed good patience to keep hold of the ball," said Cullen.
No 8 Conan was at the heart of a stifling home defence that allied seamlessly with a staggering ability to keep hold of possession for minutes on end.
Ross Byrne, standing in for the injured Jonny Sexton at flyhalf and with Rob Kearney, Robbie Henshaw, Devin Toner and Dan Leavy all also missing, kicked an early opening penalty, quickly nullified by Toulouse fullback Thomas Ramos.
A dancing Jordan Larmour break sparked an incredible 38 phases of play for Leinster over more than three minutes in and around the Toulouse 22-metre area, but the visitors, marshalled magnificently by ex-All Black No 8 Jerome Kaino, withstood the pressure.
Cheslin Kolbe was on hand with a fantastic try-saving tackle on sniping Luke McGrath, the diminutive Springbok winger managing to somehow prevent the Ireland scrum-half from grounding the ball from a five-metre scrum.
But Leinster continued to camp out deep in Toulouse territory, Conan finally crossing for the game's opening try on the other wing after a long pass had stretched a scrambling defence.
Byrne converted, but Ramos hit a second penalty at the whistle to leave a tense game 10-6 at half-time at a packed RDS Arena in Dublin.
After the break, winger Dave Kearney soared high to gather a Byrne cross-kick and somehow rode a Romain Ntamack tackle to touch down in the corner.
Hooker Sean Cronin got his name on the scoresheet, dotting down from the back of a ruck on the Toulouse line, Byrne converting for a 22-6 lead.
Adam Byrne put the icing on the cake with a fourth try for the home side, and the bonus point, after Maori All Black scrumhalf Jamison Gibson-Park threw out a monster pass from a quick penalty.
Noel Reid hit the extras, while there was enough time for Kolbe to skip away for another fine individual try he converted himself.
After Munster's 41-15 mauling of Gloucester on Friday, Ulster continued the Irish provinces' winning ways with a 26-22 victory over Racing 92, who like Toulouse had gone into the game unbeaten.
It was a wingers' first-half, with European debutant Robert Baloucoune and Jacob Stockdale crossing for Ulster, Virimi Vakatawa and ex-Munsterman Simon Zebo going over for the visitors.
Stockdale bagged his brace in the second-half as tries by Brice Dulin and Teddy Iribaren kept Racing in the game, Will Addison adding two penalties and a conversion to make the final difference.
Racing remained atop Pool 4 on 21 to Ulster's 18, having managed to bag two bonus points.
Ulster coach Dan McFarland hailed Stockdale.
"He's got a bit of stardust hasn't he?" said the Ulster boss.
Edinburgh became the first Scottish side to win at the Stade Mayol when they defeated woeful three-time champions Toulon 28-17 to stay in pole position in Pool 5, three points ahead of Montpellier who crushed Newcastle 45-8.
Toulon had led 12-8 at the interval with hooker Guilhem Guirado and Argentine back-row Facundo Isa grabbing tries while Scottish winger Darcy Graham kept Richard Cockerill's Edinburgh in touch.
Fly-half Jaco Van der Merwe kicked two penalties to nudge the visitors ahead before full-back Blair Kinghorn and centre James Johnstone crossed for tries.
All Blacks World Cup winner Julian Savea marked his return from vacation with a late try for Toulon.
