The home side, still acclimatising to life after Steve Diamond, surrendered a 12-0 advantage as Richard Cockerill's side showed their mettle to eke out a win which keeps alive their prospect of qualification and all but ends Sale's hopes.
Deacon had spoken of his desire to succeed Diamond on a permanent basis but a second defeat in as many games will do him no favours, with Alex Sanderson linked with the role.
The 41-year-old Deacon's first match in charge was a 26-14 loss at Toulon last weekend and, despite the defeat, he took heart from the performance.
On a dry but chilly evening here, the hosts gradually warmed to their task with South African World Cup winner Faf de Klerk a typically effervescent presence at scrum-half.
Indeed, there was a distinctly South African flavour to proceedings with Sale hooker, Akker van der Merwe coming up against his brother, Duhan van der Merwe, on Edinburgh's wing.
Sale also included brothers Rob Du Preez and Jean-Luc Du Preez and gave a debut to 6ft 9in lock, JP Du Preez, no relation to his new team-mates.
After Edinburgh winger Jack Blain lost the ball inside the right channel, Sale full-back Sam James sent a deft kick downfield.
From the quick line-out, Sale quickly moved the ball from left to right and Rob Du Preez's pass found Denny Solomona in acres of space. The South African's pass appeared forward but Solomona swiftly stepped inside Edinburgh full-back Blair Kinghorn and scampered over.
The try was given and Rob Du Preez applied a fine conversion to give his side a 7-0 lead after 12 minutes.
That poured confidence into Deacon's players and they scored again midway through the second half.
South African centre Rohan Janse van Rensburg collected possession in midfield and, as Mark Bennett flew out of Edinburgh's defensive line, the Sale man powered clear from just inside the visitors' half.
Edinburgh, despite scarcely venturing into Sale territory during the opening 40 minutes, somehow found themselves right back in contention 12 minutes into the second half.
It was a try chiselled on the aggressive ball-carrying of Edinburgh's forwards as they build several phases before Bennett atoned for his first-half error by bursting onto a short pass and diving over.
Jaco Van Der Walt added the conversion to cut Sale's lead to just five points and now it was Cockerill's men with self-belief surging through their veins.
As Edinburgh's replacements began to make their presences felt, Van De Walt booted a penalty in the 59th minute to move within two points of Sale.
He added another threepointer to edge the visitors in front at 13-12 and, after Van Rensburg had a try ruled out for a forward pass, Rob Du Preez added a penalty before Van Der Walt kicked another for Edinburgh to win it.
By ROSS HEPPENSTALL
Sale Sharks v Edinburgh – player ratings
SALE: S James 6 Solomona 6 (Doherty 66, 6), J Jv Rensburg 8, Hill 6, M Yarde 6, R Du Preez 7, De Klerk 7 (Cliff 76), Rodd (Harrison 50, 6), A Van der Merwe 6 (Langdon 66, 6), Cooper-Woolley 6 (Oosthuizen 50, 6), Postlethwaite 6, JP Du Preez 7 (Phillips 65, 6), Wiese 6 (Nield 65, 6), Dugdale 6, J-L Du Preez 6
Not used: Neild, L James
EDINBURGH: Kinghorn 7, Blain 6, Bennett 7 (Johnstone 69), Dean, D Van der Merwe 7, Van Der Walt 7, Shiel (Groom 48, 6) Sutherland (Schoeman 51, 6), McInally 6 (Cherry 71, 6), Berghan 6 (Nel 51, 6), Toolis 7, Hodgson 6 (Ferreira 65, 6), Bradbury 6, Watson 7, Mata 7 (Crosbie 65, 6)
REFEREE: Romain Poite
Star man: Jaco van der Walt – Edinburgh
