The striker sealed the points with a 45-yard strike, his second of the season from such a distance, that caught home keeper Alex Cairns off his line and earned a much needed three points for Stephen Robinson’s side.
The Shrimps had taken the lead in the 11th minute with an excellent free-kick from Callum Jones.
Arthur Gnahoua was fouled 20 yards from goal and Jones stepped up to drill a low shot into the bottom left-hand corner.
Morecambe stepped up the pace and went close to a second five minutes later when Stockton forced Cairns into a flying save with a shot heading for the top corner.
The home side began to settle into the game and cause the Shrimps’ defence problems.
Paddy Lane saw a weak shot easily saved by Jokull Andresson after working his way into the box.
The Morecambe keeper was then forced into a good save with his legs after Shayden Morris powered his way inside the area.
Fleetwood’s best effort of the first half came on 43 minutes when Ged Garner let fly from the edge of the box with a shot that curled inches over the bar.
Garner went close again at the start of the second half with an effort that sailed narrowly off target before Morecambe enjoyed another spell of dominance.
Jonah Ayunga saw two shots blocked and Anthony O’Connor just failed to find Alfie McCalmont inside the area.
The home side hit back with Lane forcing Andresson into a good save before Callum Johnson levelled the scores with a near post header from Danny Andrew’s corner.
Fleetwood looked the more threatening from there with Callum Morton heading another corner inches wide before the Shrimps sealed the win with Stockton’s stunner.
To make matters worse for the home side, Anthony Pilkington was sent off for two yellow cards for dissent in quick succession as the Shrimps took the spoils.
Fleetwood Town: Cairns, Johnson, Clarke (Biggins 78), Holgate, Andrew, Matete (Pilkington 78), Batty, Lane, Morris, G Garner (J Garner 68), Morton. Subs not used: Crellin, Edmondson, Clark, Johnston.
Morecambe: Andresson, McLaughlin, Delaney, O’Connor, Leigh, Jones, McCalmont, McLoughlin (Diagouraga 76), Gnahoua, Stockton, Ayunga (Phillips 79). Subs not used: Da Silva Mendes, Cooney, Gibson, Duffus, Wootton.
Referee: Darren Drysdale.
Thanks for reading. If you value what we do and are able to support us, a digital subscription is just £1 per month for the first two months. Try us today by clicking here