Liam Trotter got the breakthrough for the hosts after the break before Pigott, signed from Maidstone last week, sealed matters with 13 minutes remaining.
The Seasiders were not without chances as Dan Agyei and Sessi D’Almeida both came close.
Blackpool opened the game with an effort from Agyei whose low shot outside the box forced a save from George Long. Wimbledon’s best chance in the first half came when Lyle Taylor’s free-kick found Tom Soares whose header ended up over the crossbar.
The hosts then took the lead on 49 minutes. Cody McDonald tried his luck from the left, keeper Joe Lumley initially saved but the ball rebounded to Trotter for a tap in.
Pivotal game in Group E almost a pick ‘em with the bookies