The visitors dominated proceedings throughout the first half and were 22-0 up at the break. Having the likes of experienced campaigners Calum Cusiter, Sean McMurchy and Malcolm Clapperton back in the starting line-up helped and it was the latter who opened the scoring.
The captain took advantage of a nice pass from stand-off Greg Cottrell to go over in the corner for a try in the 13th minute and he added another two minutes later.
Muir full-back Stephen Ruddick kicked towards the touchline and Accies winger Chris Dickie kept the ball in play, but his awkward pass was missed by full-back Gavin Douglas and Ruddick pounced on the loose ball to send Clapperton over.
Then 12-0 became 19-0 in the 20th minute when a nice pass from young prop Nick Fraser sent Irish winger Ed Mills in at the corner. Centre Graeme Blackhall added a penalty before the interval after squandering two other chances.
It was a different Accies who appeared after the break, no doubt with the words of head coach Ian Barnes ringing in their ears, and they had reduced the arrears to 22-12 by the 54th minute.
The home pack looked more up for it at this stage and their hard work saw captain Dan Teague and then teenage hooker Mungo Strachan go over to set up a interesting finale.
Muir also had to deal with the loss of No.8 Lynton Brinck at this point, but they began to get back into the ascendency in the search for a bonus-point try.
They got that through replacement prop Fred Lait with five minutes to go to make it a great day at the office for the Meggetland men.
Edinburgh Accies: G Douglas; M Coupar, I Berthinussen, S Wilson, C Dickie; R Bonner, D Duffus; S Patience, M Strachan, L Niven, E Stuart, G Campbell, R Snape, D Teague, T Drennan. Subs used: D McLeod, M Stevens, J Pecqueur.
Boroughmuir: S Ruddick; E Mills, M Clapperton, G Blackhall, R Cairns; G Cottrell, C Cusiter; N Fraser, S McMurchy, B Ross, N Patrick, G Scott, M Stalley, L Brinck, J Doubleday. Subs used: F Lait, P Cronin, E Matheson, S McGhee, D Murray.
Scorers: Edinburgh Accies: Tries: Teague, Strachan. Con: Douglas. Boroughmuir: Tries: Clapperton 2, Mills, Lait. Pen: Blackhall. Cons: Blackhall 3.
Referee: D Jack.