Saints were 21-19 down with five minutes left when Easter delivered.
Full-back Bruce Reihana weighed in with 14 of Northampton's points with two tries and two conversions, while winger Ben Cohen also added a try.
Olly Barkley contributed 11 points for Bath, converting Joe Maddock's try and kicking three penalties after Salesi Finau had opened Bath's account.
Bath boss Brian Ashton:
"I'm very frustrated and disappointed with the way we lost it. "We got our noses in front and looked as though we were going to score another try, but then we missed a tackle and lost it.
"Since I've been back at Bath no side in the Premiership has attacked us as consistently as Northampton did.
"(Saints fly-half) Carlos Spencer is a special talent. He plays rugby totally differently to any other player in that position in the world."
Northampton: Reihana, Lamont, Clarke, Quinlan, Cohen, Spencer, Robinson, Smith, Thompson, Barnard, D. Browne, Lord, Tupai, Harding, D. Browne.
Replacements: Richmond for Thompson (69), Budgen for Barnard (60), Lewitt for Tupai (60), Easter for D. Browne (69). Not Used: Gerard, Howard, Kydd.
Bath: Maddock, Finau, Crockett, Barkley, Higgins, Malone, Williams, Flatman, Dixon, Filise, Borthwick, Grewcock, Short, Lipman, Delve.
Replacements: Abendanon for Maddock (72), Fuimaono-Sapolu for Malone (41), Bell for Flatman (50), Mears for Dixon (60), Fidler for Borthwick (77), Fea'unati for Lipman (70). Not Used: Fulton.
Att: 13,454