Saracens dominated the game but the teams were 9-9 going into the last 10 minutes after three penalties each from Jackson and Bath's Andy Dunne.
And Bath looked to have snatched the points when debutant Michael Stephenson fired over a drop goal.
But Jackson kicked his fourth penalty to make the scores level before missing two injury-time drop goals.
Saracens coach Steve Diamond:
"As a game it wasn't pretty and I felt sorry for the crowd. "Fair play to Bath, with so many players out they battled hard. Our mindset wasn't 100%.
"But I was frustrated, not only with our performance but also with the referee and the way he dealt with them at our rolling mauls."
Bath: Best; Maddock, Higgins, Crockett, Stephenson; Dunne,
Walshe; Barnes, Dixon, Bell; Fidler, Short; Beattie (capt), Lipman,
Fea'unati.
Replacements: Williams for Walshe (28), Delve for Short (62), Scaysbrook for Lipman (62).
Not Used: Hawkins, Loader, Cheeseman, Smith.
Saracens: Scarbrough; Haughton, Bartholomeusz, Sorrell, Bailey;
Jackson, Bracken; Yates, Cairns, Visagie; Raiwalui, Fullarton;
Vyvyan (capt), Seymour, Skirving.
Replacements: Vaikona for Bailey (55), Dickens for Bracken (60), Kyriacou for Yates (67), Chesney for Raiwalui (50), B Russell for Seymour (78).
Not Used: Broster, B Russell.
Att: 10,346.
Ref: Ashley Rowden (RFU).
MMIX
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