Owned by Rich Ricci and ridden by Paul Townend, the six-year-old, who started his career by winning a four-year-old maiden at Stowlin for Cormac Doyle, rallied gamely in the closing stages to deny the Paul Nolan-trained Latest Exhibition (9/2) by a neck, with Gordon Elliott's Fury Road (5/1) a further nose behind in third.
Mullins had already hit the scoresheet this afternoon with Burning Victory (12/1, G1 JCB Triumph Hurdle) and Saint Roi (11/2 favourite, G3 Randox Health County Hurdle).
He is the leading trainer of all time at The Festival with this being his 71st winner in total.
He said: "Monkfish looks a real chaser. I don't think the race went according to plan for Paul - he was just doing a little too much for him but he found himself there.
"I thought Paul gave him a fantastic ride to extract him out behind the two horses. I thought that we were settled for third when they passed him after jumping the last but Paul really drove him up the hill. I am delighted for Paul to get a winner in that fashion.
"Monkfish is maturing all the time and Paul said that he felt there is still more to come - he said you could feel the power coming when he got after him.
"He is a huge, big horse but, if he has to come back and win a Stayers' Hurdle, we won't complain either."