The 24-year-old right-back netted the only goal of the game in the 24th minute with a fierce left-footed strike from the edge of the box that cannoned in off the underside of the bar.
Accrington could only muster half-chances from Peter Murphy and Francis Jeffers in response as leaders Gillingham took full advantage of the depleted League Two fixture list.
They are now eight points ahead of second-placed Port Vale and Allen admitted not even he expected Fish to deliver the winner as he begins to dream of promotion to League One.
"I've never even seen Matt kick it with his left foot but then he nearly broke the crossbar," said Allen. "(It was an) Unbelievable shot, went in like a missile.
"And what a great moment that was for him, he's been fantastic this season and he keeps getting better and better. He's a top lad on and off the field.
"It's the players that deserve all the credit, they've been absolutely fantastic since day one. I thought we were absolutely fantastic in the first half.
"I've been waiting 17 years for this. I've always been the mad dog fighting to keep clubs out of relegation and all of a sudden we're looking into what could be a fantastic Easter.
"It's been unbelievable for me personally. I've been lucky enough to get some clubs into the play-offs but to be top of the league by eight points, I have to pinch myself."