Jackson, the Gills' top scorer, got free at the back post to head home a Josh Wright corner for his 21st goal of the season in the League Two play-off final at Wembley.
And the Canadian will have scored few more priceless, this one securing promotion for the Gills just a year after their relegation to the basement division.
Replays showed that the corner should not have been given, but the Gills will not care, with the Shrews having dominated the second half at Wembley.
Their best chance fell to Kevin McIntyre but he headed wide, while Shrewsbury goalkeeper Luke Daniels had kept his side in it at the break with fine saves from John Nutter and Wright.
The first 20 minutes passed with little more than mild panic at either end, but slowly it was Gillingham who got a grip on the encounter even if their attacking threat was nullified by the Shrews defence.
Shrewsbury captain Graham Coughlan diverted a Nutter free-kick just past his own post, and from the corner Wright fired over the top.
Gillingham were almost in again when some smart play ended with Barry Fuller's cross being flicked on by Dennis Oli and Neil Moss tidied up well at the back post.
The Gills worked the next corner well as Andy Barcham left the ball for Nutter, whose powerful shot was diverted over the top by a combination of Grant Holt and goalkeeper Daniels.
Shrewsbury's first real effort came 10 minutes before the interval when Garry Richards fouled Nick Chadwick and Ben Davies - from fully 30 yards - sent the free-kick just wide.
But Daniels was at it again in stoppage time of the first half, diving low to his right to claw away a Wright shot through a crowd of players.
The second half started in a similar fashion as Barcham wriggled free and cut inside before unleashing a right-foot shot which was bound for the top corner, but Daniels pushed it away.
Gills keeper Simon Royce made his first save of note not long after when a long Graham Coughlan free-kick was headed on by Kelvin Langmead for Davies to strike goalwards, but Royce clung on.
And Langmead caused problems with another towering header across goal, but Kevin McIntyre's diving header was horribly wide.
Shrewsbury were notably better after the break, and the game benefited for that, becoming a much more open contest.
A smart move gave Davies a clear run at goal, but his touch was heavy, allowing Barcham to get back and make a saving challenge, and Royce saved Langmead's header from the resulting corner.
But after weathering the storm, the Gills took the lead as stoppage time approached from a Wright corner, which Jackson headed home despite the efforts of Ashton on the line.
The Shrews threw everyone forward and Davies crossed for Coughlan, but he headed over the top, and the Gills held on for promotion.