Edinburgh moved level on points with Ulster and Stade FranÃ§ais on Saturday after a scrappy 9-6 victory condemned Bath to the foot of Pool Four.
Much had been made of the need for the Scots to make a good start to this contest and Chris Paterson made sure they did with a fine kick to Bath's right corner.
Bath won the lineout and Nicky Little got his kick away but not to touch and as the ball was brought back Bath were penalised at a ruck set up by Nick De Luca and Paterson did the needful from in front of the posts in the second minute.
Bath got a chance to equalise the score three minutes later. Edinburgh scrum-half Greig Laidlaw chipped a clearing kick to midfield where Edinburgh went over the top at the ruck. Little's kick was on target but low.
Home centre Ben Cairns brought the crowd of 5,238 to life when he hared down the left wing in pursuit of his own kick and forced an Edinburgh lineout ten metres out.
In the subsequent play Edinburgh were awarded a penalty but rather than take the kick captain Paterson went for a lineout which came to nothing.
Edinburgh's spell of fruitless possession came to an end when number ten Phil Godman dropped a pass in midfield.
This allowed Bath to get on to the front foot but when Ross Ford charged down a drop-goal attempt by Nick Abendanon they seemed to be weathering the storm.
However, in the 21st minute - just as the promised snow arrived - Fijian playmaker Little kicked the equalising penalty.
This unsettled Edinburgh and they gave away two further penalties - Little was successful with the second on the half hour.
But no sooner were Bath ahead than they gave away a penalty soon after the restart and Paterson struck the straightforward kick home and the teams turned drawing 6-6.
With the snow off the game restarted with Edinburgh much more focused.
Benefiting from touch kicks by Paterson plus pick and go by the forwards they camped in Bath territory.
However, the visitors' defence was solid - particularly scrum-half Michael Claassens who was first to the ball when Edinburgh drove a scrum under his posts.
In the closing stages Bath sub Ryan Davis missed two penalties, while Godman was off-target with one from long distance.
Pen: Paterson 3
Pen: Little 2
Edinburgh: 15 Chris Paterson (c), 14 John Houston, 13 Ben Cairns, 12 Nick De Luca, 11 Tim Visser, 10 Phil Godman, 9 Greig Laidlaw, 8 Scott Newlands, 7 Ross Rennie, 6 Alan MacDonald, 5 Craig Hamilton, 4 Steve Turnbull, 3 Geoff Cross, 2 Ross Ford, 1 Kyle Traynor.
Replacements: 16 Andrew Kelly, 17 Allan Jacobsen, 18 David Young, 19 Scott MacLeod, 20 David Callam, 21 Ross Samson, 22 Mark Robertson, 23 Jim Thompson.
Bath: 15 Nick Abendanon, 14 Michael Stephenson, 13 Matt Carraro, 12 Shontayne Hape, 11 Tom Cheeseman, 10 Nicky Little, 9 Michael Claassens (capt), 8 Luke Watson, 7 Julian Salvi, 6 Andy Beattie, 5 Peter Short, 4 Stuart Hooper, 3 David Wilson, 2 Pieter Dixon, 1 David Flatman.
Replacements: 16 Lee Mears, 17 Nathan Catt, 18 Duncan Bell, 19 Danny Grewcock, 20 Ben Skirving, 21 Scott Bemand, 22 Ryan Davis, 23 Jack Cuthbert.
Referee: Romain Poite (France)
Assistant referees: CÃ©dric Marchat (France), StÃ©phane Boyer (France)
Television match official: Jean-Christophe Gastou (France)