The Irish trailed 43-3 in the 59th minute and appeared on course for a record defeat by France, who were making the most of an error-strewn display from their opponents.
But four unanswered tries from Ronan O'Gara, Gordon D'Arcy, Donncha O'Callaghan and Andrew Trimble saw French eyes glance nervously towards the scoreboard with 10 minutes to go.
The ease with which Ireland were shredding the home defence gave genuine hope they could complete one of the greatest fightbacks in rugby history.
Bernard Laporte's side, frequently jeered by their own fans when they made a mistake themselves, were forced to repel waves of attacks but held firm for a 43-31 win, their first of the 2006 RBS 6 Nations Championship.
It was a magnificent response from Ireland and Murphy, one of the forces behind the revival, admitted his side would be title contenders if they could maintain that intensity for 80 minutes.
"We wanted to play an expansive game and take them on but anything that could go wrong did in the first half," he said.
"We went in at half-time and Eddie was calm and told us we'd played all the rugby. At that point not one of their tries had been scored through their own initiative.
"Eddie was happy and said we'd played well apart from the mistakes which led to the tries. He told us Irish teams have let their heads drop in the past and were beaten at the gate.
"We were told not to let that happen and to play for each other. They scored again in the second half but still our heads didn't drop. Then we started playing some good rugby and it started to click.
"There were a lot of Irish guys who were dead on their feet at the end but France were absolutely knackered. If we could play like that second half in every game, we'd be doing very well.
"We'll frighten a few teams if we put a whole game together like that. That's the aim. We've been promising to deliver a game for a while now and we want to play 15-man rugby."