Yet it was the visitors who struck first after 11 minutes when an inswinging corner was cleared only as far as Steve Brodie who swept the ball into the roof of the net.
Less than two minutes later Boro defender Richard Lavery was given his marching orders after being adjudged to have raised his hand towards Neil Grayson.
With the one-man advantage Rovers pushed forward for the equaliser with Kayode Odejayi's headed flick-on from Alex Sykes' corner bouncing off the post.
In the 23rd minute Meechan's corner fell to Forest Green defender Darren Jones but his shot on the turn was well saved by Boro keeper Chris MacKenzie who parried the ball behind the goal.
From the resulting corner Grayson's flick-on found Meechan at the back post to fire beneath the keeper.
In injury time Meechan grabbed his and Rovers' second after racing onto Kevin Langan's long ball forward before curling the ball into the left-hand corner of the net.
It took just nine minutes of the second half for Meechan to grab his hat-trick, this time latching onto Sykes' pass and spinning past his marker before slotting the ball into the far corner of the net.
Just after the hour Rovers were awarded a penalty after Michael Love brought Grayson down in the box and although Grayson's first attempt was saved MacKenzie was adjudged to have moved off his line too soon and Grayson sent him the wrong way from the retake.
With 17 minutes left former Boro player Sykes got his name on the scoresheet firing Odejayi's lay-off into the right-hand corner from the edge of the area.
Grayson finished off the rout in injury time with a header into the top right-hand corner from Steve Cowe's right-wing cross.