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In an entertaining game, strike partner Steve Kabba had three goals disallowed and Saints midfielder Adam Lallana saw two efforts cleared off the line.
A lively opening 20 minutes witnessed some frantic end-to-end football as first Lee Holmes drove down the left-hand side for the home side and his cross was punched by Paul Rachubka for Lallana's goal-bound follow-up to be hacked clear by Rob Edwards.
Lallana was again involved just two minutes later as he found space amid a crowded penalty area and drove once more towards goal but this time he was denied by Ian Evatt.
At the other end some lacklustre Southampton defending allowed Taylor-Fletcher a free strike on 18 minutes but Davis was his equal to it, making a smart low save.
Moments before the break Blackpool hit the home side with a real sucker-punch as Taylor-Fletcher dropped a shoulder to Simon Gillett before tempting White into his rash challenge, and Burgess duly obliged from the penalty spot.
As they chased for an equaliser in the second half, Southampton's young legs became heavier and Blackpool consequently exploited the space behind.
Kabba was denied on three occasions by referee Andre Marriner, twice for a foul on Davis and then for offside.
Burgess then could have wrapped the game up on 70 minutes when he received a superb pass from David Fox only to be denied by Davis.
The powerful Blackpool striker then wasted another good opportunity as he turned Chris Perry before clipping the far post.
Southampton's only real chance fell to David McGoldrick in the final minute as he burst into the penalty area but blasted his shot against the frame of the goal.