From the first meaningful attack off set piece in the 11th minute Saracens opened the scoring with a simple miss one backline move that left Rodd Penney with a straight forward run in on the left.
However two tries in as many minutes from Danny Grewcock and Andy Beattie both converted by Olly Barkley put the visitors 14-5 in front.
A period of pressure initiated by a good Shane Byrne break ended with a Glen Jackson penalty for Saracens and moments later with numbers over, and a try looking on, Saracens glee turned to horror when David Bory intercepted to race half the length of the field and score under the posts (21-8).
From the restart slick handling and neat footwork sent Penney in for his second try and when Bath messed up the restart by kicking straight into touch Saracens attacked from the scrum and Joe Maddock just beat Dan Scarborough to the touchdown.
Next up for Saracens was Thomas Castaignede to breach the Bath defensive line and when he was hauled down just inside the Bath half, the penalty was conceded and Jackson knocked over a massive kick to leave his side trailing by just three points (21-18).
However deep in injury time Bath struck again, out-half Shaun Berne breezing through half-hearted defence to score his side's fourth try, Barkley converting to leave Bath 28-18 in front at the interval.
Three minutes after the restart Jackson should have reduced the arrears with a simple enough penalty but immediately after Saracens moved the ball left and right before Scarborough scored a stunning try. Jackson was on the mark this time and Sarries trailed by three again (28-25).
That lead became six when Barkley converted a penalty after Saracens were penalised for not rolling away and it remained like that until ten minutes from time when Scarborough went over in the right corner after the TV official had ruled out an effort on the left.. Jackson missed with the difficult conversion and Bath held on for the narrowest of victories
Saracens: Thomas Castaignède; Dan Scarbrough, Kevin Sorrell, Andy Farrell; Neil de Kock (Alan Dickens), Glen Jackson; Rodd Penney; Ben Skirving, Richard Hill (David Seymour 59 min); Simon Raiwalui (Ian Fullerton 62 min), Hugh Vyvyan; Kris Chesney, Cobus Visagie (C Johnston), Shane Byrne (Matt Cairns 65 min), Nick Lloyd
Bath: Joe Maddock, Tom Cheeseman, Eliota Fuimaono-Sapolu, Olly Barkley, David Bory; Shaun Berne, Nick Walshe; Isaac Feaunati, Michael Lipman, Andy Beattie (Peter Short 62 min) , Danny Grewcock, Steve Borthwick (c); Matt Stevens, Lee Mears, David Barnes.