Bath (13) 16
Tries: Dixon, Stephenson Pens: Little 2
Edinburgh (9) 9
Pens: Paterson 3
Michael Stephenson crosses in the corner as Bath claim a much-needed win
Bath hung on desperately to record a crucial win over Edinburgh which keeps their Heineken Cup hopes alive.
The home side started the game well and hooker Pieter Dixon bundled over early on with Nicky Little adding a penalty.
Edinburgh full-back Chris Paterson reduced the deficit with two penalties but Michael Stephenson crossed in the corner to extend Bath's lead.
The Scottish side piled on the pressure in the closing stages but Bath held out for their first Pool Four victory.
The home side, who went into the match with only one win from their previous 11 games, started off with real intent and after some nice work from wing Stephenson and full-back Nick Abendanon, Dixon just managed to barge his way over the line on three minutes - the video referee awarding the try.
Fly-half Little extended the lead four minutes later with a penalty after Edinburgh were penalised for going into a ruck off their feet but the ever-accurate Paterson replied with six points of his own.
Bath scored a second try on the half-hour mark, Stephenson played in at the corner by Jack Cuthbert, in the side for the suspended Matt Banahan, after a patient build-up involving numerous phases.
Edinburgh lost fly-half Phil Godman to the sin-bin for talking back to referee Alain Rolland on 34 minutes but despite being down to 14 men, the visitors almost stole a try a minute later.
Centre Nick De Luca ran half the length of the field after a perfectly-timed interception as Bath pressed but the home defence got back superbly to snuff out the danger.
Paterson did add a third penalty just before the break, however, when Bath centre Shontayne Hape was penalised for a high tackle.
The second half was not as free-flowing as the first, with Bath having the better of the play but not being able to break down the Edinburgh defence.
The misfiring Little had a chance to put Bath further in front but his penalty from just inside the Edinburgh half on 66 minutes came back off the bar.
It was his fourth miss out of five attempts but he settled down seven minutes later to sneak a kick just inside the uprights.
Edinburgh refused to give in, however, and Tim Visser's neat step and break on the left wing kick started a spell of intense pressure late on.
The visitors battered the Bath line and the home side thought they had sealed the win but after turning the ball over, it was mistakenly passed straight out of play and Edinburgh were able to go again.
They threw everything forward but Bath's defence stood firm to seal a morale-boosting win.
Bath head coach Steve Meehan:
"We made a terrific start. There was great intent from the guys and we want to see more of that.
"It's terrific to see the effort transferred from the training field to the pitch. But it's very important that it is maintained.
"It's great to be travelling to Edinburgh at the end of this week with an opportunity. Conditions being fine, you'd expect another entertaining game."
Edinburgh head coach Rob Moffat:
"Looking at the whole game, we weren't as accurate as we should have been. The way we started lost us the game.
"I am frustrated with our first-half display. Bath looked sharper than us and going eight points down didn't exactly help.
"We got turned over too many times and made elementary mistakes. We had to work hard in defence, coughing up ball after two or three phases, and we didn't put Bath under enough pressure.
"It was a good game, with plenty of action but we weren't good enough on the day. All we can do now is try to win our last three games, starting with Bath at home next week. We'll look forward to it."
Bath: Abendanon; Stephenson, Carraro, Hape, Cheeseman; Little, Claassens; Flatman, Dixon, Wilson, Hooper, Short, Beattie, Salvi, Watson.
Replacements: Bell for Wilson (68), Skirving for Beattie (69).
Not Used: Catt, Hobson, Bemand, Davis, Williams, Lilley.
Edinburgh: Paterson; Houston, Cairns, De Luca, Visser; Godman, Laidlaw; Jacobsen, Ford, G Cross, S Turnbull, MacLeod, MacDonald, R Grant, Newlands, D Blair.
Replacements: Thompson for Paterson (65), D Blair for Godman (55), Traynor for Jacobsen (58), Kelly for Ford (68), Young for G Cross (79), C Hamilton for S Turnbull (40), Hogg for Newlands (60), Samson for D Blair (77).
Sin bin: Godman (34)
Ref: Alain Rolland (Ireland).