Jersey came away from Plymouth with a second British and Irish Cup win.
The home side scored an early try through Marc Koteczky's before he and Aaron Penberthy traded penalties.
Jersey took a 10-8 lead into half-time after Tobias Hoskins went over against the run of play and Penberthy added two penalties either side of the break.
Rob Langley's try gave Albion hope and they were level from Koteczky's second kick before Penberthy got a penalty and a drop goal to win the game.
The victory pulled Jersey level with Leinster 'A' at the top of Pool Five after the Irish side lost 26-24 at Carmarthen Quins.
Koteczky went over after three minutes, following good work from Iain Grieve and player-coach James Shanahan, but missed the conversion.
After trading penalties Penberthy missed a long-range effort on 26 minutes as Albion piled on the pressure.
But Jersey went off at half-time with the lead after one of their few forays into the Albion 22.
Tobias Hoskins scored on 37 minutes after a break from Grant Pointer set up David Bishop, whose reverse pass allowed the Australian to get his first try for the island side since joining in the summer.
Penberthy then added two more penalties either side of half-time, the first after Shanahan was sin-binned for a deliberate knock-on.
But despite only having 14 men Albion started the second half stronger and Rob Langley went over in the right corner after a Jersey mistake from the line-out.
Albion should have sealed the win as Tom Cowan-Dickie and Ben Woods both failed to go over from good positions.
Koteczky made it 16-all with a penalty on the hour mark before Penberthy kicked Jersey ahead six minutes later.
Albion's Australian full-back then missed from right in front of the posts with seven minutes left to set up a tense finish, which Jersey reacted best as Penberthy calmly slotted over what proved to be the winning drop goal three minutes from time.
Plymouth Albion: Marc Koteczky, Lewis Warner, Ben Woods, Toby Howley-Berridge, Peter Homan, James Shanahan, Josh Davies; James Gibbons, Ted Stagg, Tom Heard, Rhys Oakley, Brett Beukeboom, Herbie Stupple, Rob Langley, Iain Grieve (capt).
Replacements: Tom Cowan-Dickie, Dan Pullinger, Tom Hicks, Tom Fidler, Eoghan Grace, Cameron Setter, Lawrence Rayner.
Jersey: Grant Pointer, Mark Foster, David Bishop, Tobias Hoskins, Mark McCrea, Aaron Penberthy, Joel Dudley; Ignacio Lancuba, Gareth Harris, Danny Herriott, Nick Campbell, Dave Markham, Alex Rae (capt), Joe Buckle, Michael Noone.
Replacements: Martin Garcia-Veiga, Jon Brennan, Nick Haining, Ryan Hodson, Ryan Glynn, Lewis Robling, Jack Burroughs.