Barnsley 2 Blackpool 1
The 21st-minute spot-kick gave Barnsley captain Brian Howard his seventh goal of the season but Blackpool's troubles deepened when Jackson was sent off for a second bookable offence after 52 minutes.
Barnsley cashed in with a second goal when Hungarian striker Istvan Ferenczi headed in a 70th-minute effort before Keith Southern pulled one back for the Seasiders two minutes later.
The victory pushes Barnsley into the play-off zone - at least for 24 hours - as they continued an impressive home run that has seen them unbeaten at Oakwell since the first day of the season.
Barnsley were second best in their second game in three days until the referee gifted them a disputed penalty when Sam Togwell went down under Shaun Barker's challenge even though he had already played the ball wide.
After Blackpool's protests had been waved away, Tykes skipper Howard drilled in the penalty squeezing his shot inches away from Paul Rachubka's dive.
It was tough on struggling Blackpool who were fresh from a free weekend and looking for their first league win for two months.
But for early saves from Barnsley keeper Heinz Muller, Simon Grayson's side might had snapped up an early lead.
Two efforts from Gary Taylor-Fletcher failed to beat Muller as the German keeper held a low shot and then blocked a bullet header.
Keigan Parker went close again two minutes into the second half when he smashed a 25-yard effort that skidded off the surface but Muller managed to turn it away for a corner.
Jackson was booked for a first-half foul on Howard but when Ferenczi went down under a crunching challenge he was dismissed.
On the break Blackpool still caused problems and Parker crashed a rising 25-yard shot that had Muller at full stretch to turn it over the bar.
But the Blackpool defence finally cracked when Ferenczi turned in a towering header from Howad's free-kick only for Southern to pull one back with a 12-yard shot after Muller's poor punch.
And in a spirited Blackpool fightback, Muller had to produce a great save to stop Scott Vernon grabbing a late equaliser.