But against Bath, a dominant performance from their pack and a metronomic kicking display from Madigan saw them triumph 18-12 at the Aviva Stadium.
An ill-disciplined first-half display from the English side meant they trailed 15-5 at the break despite a spectacular solo try from George Ford.
A scything break by Ford after the interval saw him offload for Stuart Hooper to touch down, only for Madigan to boot his sixth penalty.
Ford's penalty then set up a dramatic finish but the hosts held firm to come out on top and Madigan believes the win could prove to be season-defining.
"This victory means everything to us, our season really rolled on this game," said the Ireland international.
"We've had mixed form in the league but our preparation leading into this game was exceptional.
"It might not have been the prettiest performance at time but we're delighted to get the win and I thought the support we got was fantastic.
"Bath are a really good side - they've got international players across their team and they really tested us throughout the 80 minutes.
"It means a huge amount to us to still be in Europe. Leinster have proven over the last five, ten years that we're a knockout side and when it's a knockout game then we can win."
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