Edinburgh lie 11th in the RaboDirect PRO12 while Toulouse are top of the French league yet the Gunners were determined not to be bullied in front of a crowd of 37,881.
A try in the second minute through scrum-half Mike Blair got them off to the best possible start at Murrayfield.
Laidlaw hoisted a high ball and Toulouse wing Timoci Matanavou Edinburgh profited from Toulouse failed to collect it allowing Blair to pounce on the loose ball to crash over.
Laidlaw converted but three Lionel Beauxis penalties gave Toulouse a 9-7 lead before Matanavou stepped through Edinburgh's forwards and used his speed to out-run the cover defence for a superb individual try.
The hosts were then reduced to 13 men after yellow cards for prop Allan Jacobsen and flanker Ross Rennie but Laidlaw steadied the ship with a long range drop-goal.
The tables turned in the second half after Toulouse hooker William Servat was sent to the sin bin, Edinburgh seized their chance with two Laidlaw penalties and the French side were left shell-shocked.
The Gunners then dominated possession and territory, limiting Toulouse to a couple of desperate attacks at the end before Laidlaw sealed the deal with a late penalty.
Edinburghwill now play either Munster or Ulster in Dublin on Saturday 28 April for a place in the final.
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