The visitors opened the scoring when Grant McConnell gathered a cross kick from Chris Laidlaw to touch down in the corner.
Jamie Forbes clawed back three points with a penalty then added the conversions after wingers Cammy Gray and Ben Robbins had bagged a try apiece for a 17-5 interval lead.
Boroughmuir restarted with intent but failed to convert ten minutes of sustained pressure into points. Having survived that spell on the back foot, Currie moved further ahead when Harvey Elms dotted down in the corner.
The bonus point came in 66 minutes when a powerful surge from the home pack at a scrum shunted the opposition eight backwards and allowed Fergus Scott to apply the final touch.
The visitors responded with a similar effort from Thomas Gracie with ten minutes to play but any hopes of an unlikely fight back were extinguished when Reece Patterson forced his way over for a fifth Currie try.