After a goalless draw at Spotland, the game on the Kent cost was a winner-takes-all encounter with Gillingham having the advantage of playing in front of a packed house.
Jackson netted either side half-time to send Mark Stimson's side to a meeting with Shrewsbury Town.
Gillingham had the better of the opening exchanges and the Priestfield Stadium was rocking after 13 minutes when Jackson poked home his first from close range.
It was the striker's 19th goal of the season, and came about after Dennis Oli played in Andrew Barcham on the left. His first-time cross was met by Jackson at the near post and he was able to steer the ball home past Frank Fielding in the Rochdale goal.
The Gills looked the better side after the goal and Barcham had a chance to double the lead on the half-hour when he beat three defenders on a powerful run, but opted to shoot when Jackson was unmarked and his effort was blocked by Rory McArdle.
Rochdale made them pay for that miss just before half-time when Chris Dagnall levelled the tie.
Dagnall - who was Dale's brightest player - received the ball after Joe Thompson's shot had fallen into his path after bouncing off Barry Fuller. The striker then twisted and turned John Nutter inside out before smashing the ball past Simon Royce.
But Gillingham came out the brighter for the second half and retook the lead when Nutter's goal-bound run was brought to an abrupt halt by Rory McArdle and referee Michael Oliver had no hesitation in pointing to the spot.
Jackson made no mistake from 12 yards, sending Fielding the wrong way with a powerful strike.
The Gills could have made the game safe just minutes later when Garry Richards saw his header come crashing back off the crossbar.
But the miss did not matter as Gillingham held on to book their place at Wembley in a fortnight's time.