Febian Brandy was brought down by Stefan Sam to win his third penalty in four matches and Jackson made no mistake in coolly chipping the spot kick past Alex McCarthy.
Manchester United loanee Brandy hit the crossbar after 22 minutes and McCarthy produced a superb double save eight minutes later as Gillingham pressed for a second.
Yeovil produced their first shot on goal, but Sam Williams' effort was high and wide. McCarthy superbly touched Barry Fuller's 25-yard free-kick on to the post after 63 minutes.
Gillingham goalkeeper Simon Royce hit Williams' header over the crossbar at the other end as the visitors searched for an equaliser, but Yeovil's misery was compounded in the 79th minute when Jean-Paul Kalala was sent off for a second bookable offence.