Sonny Carey and Kylian Kouassi were both on the scoresheet for the Seasiders at Holker Street.
Neil Critchley made nine changes to the side that overcame Wigan Athletic at the weekend, with only Callum Connolly and Jensen Weir remaining in the starting 11.
Blackpool dominated the first half, but struggled to create too many clear opportunities.
Dembele fired a couple of shots off target, while Owen Dale had an attempt deflected wide.
The opener eventually came in the 44th minute, with Carey calmly moving the ball onto his right foot before curling a shot past Josh Lillis.
In the second half, Barrow gave the Tangerines a much sterner test.
The closest chance they had came through Courtney Duffus, who forced a superb save from Richard O’Donnell.
Despite the Bluebirds’ pressure, the Seasiders were able to confirm the victory heading into the latter stages, with Kylian Kouassi marking his debut with a goal, after a good break down the right side from Albie Morgan.
Here is how the Seaisders performed:
1. Richard O'Donnell- 8
O'Donnell made a superb save in the second half to preserve the Seasiders' lead. Photo: CameraSport - Andrew Kearns
2. Doug Tharme- 7
Doug Tharme was solid in his first start for the club, with some commanding moments in the air. He did have to be more careful after being booked towards the end of the first half. Photo: CameraSport - David Horton
3. Marvin Ekpiteta- 7
It was a solid enough display from the centre back. Photo: CameraSport - Dave Howarth
4. Callum Connolly- 8
Connolly was a rock for Blackpool once again, with a number of important contributions. Photo: CameraSport - Alex Dodd
5. Jensen Weir- 7
Weir enjoyed some bright moments down the right side. Photo: CameraSport - Dave Howarth
6. Kenny Dougall- 7
Dougall provided a good link between defence and attack. Photo: CameraSport - Dave Howarth