Malone's two extra conversions and drop goal constituted the seven points between the two teams at the end of the contest, although Bath had the game sewn up after a surge at the start of the second half.
Bath opened the scoring with a try by debutant Frikkie Welsh just nine minutes into his first game in a Bath shirt. Barkley converted, but went off injured ahortly afterwards.
Saracens responded with tries by Hugh Vyvyan and Robbie Kydd. Vyvyan capitalised on untidy Bath lineout play, and Kydd fed off a superb cross kick by Mark Bartholomeusz.
Kydd converted his own try and Sarries were 12-7 ahead after the first quarter of the game.
Malone and Kydd traded penalties, and shortly before half-time, young winger Andy Higgins crossed the line, having hacked on a careles Bartholomeusz pass. Malone added the extra points to put Bath into the lead again.
Kydd slotted a pwnalty for Saracens, and Malone added a drop goal for Bath, and then landed another penalty for a half-time Bath lead of 18-23.
Bath surged to an uncatchable lead in the first 20 minutes of the second half. Welsh scored again six minutes in, then England's Mike Tindall marked his recent good form with a try under the posts on the hour.
Malone converted both, and the score was 18-37.
Glen Jackson and Moses Rauluni responded with tries for Saracens, and Jackson's conversion of his own try in the 75th minute gave the Saracens a deserved bonus point from a thrilling game.
For Saracens:Tries: Vyvyan, Kydd, Rauluni, JacksonCons: Kydd, JacksonPens: Kydd 2
For Bath:Tries: Welsh 2, Higgins, TindallCons: Barkley, Malone 3Pens: Malone 2Drop goals: Malone