The victory sees the Seasiders finish top of their EFL Trophy group and progress to the next round- which will be played at the beginning of December.
Neil Critchley named a number of youngsters in his matchday squad, with some of them able to impress against the Shrimps.
Following a quiet opening period, Blackpool took the lead in the 22nd minute.
With his back turned away from goal, Beesley got on the end of a Jensen Weir cross to guide a volley past Adam Smith in the Shrimps net.
Chances continued to be limited throughout the first half, with an easy save from an Andy Lyons shot from distance being the closest either team came to getting the second goal of the game before the break.
Following the restart, the Seasiders quickly doubled their lead.
Beesley met another cross from the left side, with the striker using his head this time to beat the Morecambe keeper.
Down the other end, substitute Tayt Trusty came close to extending Blackpool’s lead, with his effort being cleared off the line.
Shortly after, the youngster was forced off on a stretcher after suffering what appeared to be a knee injury.
Morecambe pulled a goal back in stoppage time, with Farrend Rawson heading past Richard O’Donnell to make it 2-1.
Here’s how the Seasiders performed:
1. How did Neil Critchley's side perform against Morecambe?
We've taken a look at how the Seasiders performed in the EFL Trophy tie at Bloomfield Road. Photo: CameraSport - Lee Parker
2. Richard O'Donnell - 7
There wasn't too much for Richard O'Donnell to do, as he continued his run between the sticks in cup competitions for the Seasiders. He did make a great save ahead of the 70-minute mark, but the linesman's flag was up regardless. Photo: CameraSport -
3. Doug Tharme- 7
It was a solid night for Doug Tharme, who has become a regular in the EFL Trophy. The defender made some key contributions at the back, and also played some good balls forward. Photo: CameraSport -
4. Olly Casey- 9
Olly Casey was named as captain on his return from suspension. The centre back led the team well, especially with him being one of the more experienced players in the team. He more than deserved the armband. Photo: CameraSport - Dave Howarth
5. Will Squires- 8
Will Squires was back in the team after previously appearing against Liverpool U21s. He produced an excellent display, and looked solid in the back three. Photo: CameraSport - Lee Parker
6. Jordan Lawrence-Gabriel- 7
Jordan Lawrence-Gabriel was handed his first appearance of the season following a lengthy absence through injury. It was a solid display from the wing-back throughout the first half, before he was subbed at the break. He'll certainly have a big role to play this season. Photo: CameraSport - Lee Parker