Reid pulled back striker Keigan Parker who looked set to grab a late winner for struggling Blackpool, a move which won favour with the manager.
Barnsley had started the brighter but found themselves behind on 20 minutes when Parker charged through the heart of the defence before being hauled down just outside the area by defender Neil Austin.
Parker stepped up, dusted himself down and hit the resulting free-kick into Nick Colgan's top right-hand corner.
Parker again troubled the Tykes by breaking away down the right courtesy of a superb turn against former Blackpool target Paul Heckingbottom and swung a long cross which strike partner Gareth Williams saw well saved by Colgan.
At the other end Daniel Nardiello had a rare sight of goal in injury time but hit his first-time volley was well over the bar after a good pass by the impressive Chris Shuker.
Barnsley came out with a renewed sense of purpose after the break and took just seven minutes to find an equaliser.
Paul Hayes swung in a far post cross which was headed back across goal by Nardiello for Shuker to take a shot which Lee Jones did brilliantly to save but the ball fell kindly for Brian Howard and the little midfielder headed in to the empty net.
That seemed to wake Blackpool up once again and they almost grabbed all three points when midfielder Marcus Bean got on the end of a superb cross by former Oakwell trainee Rory Prendergast but he could only steer his shot a yard wide of the unguarded net.
In the last minute Reid should have clipped the ball into touch under pressure from Parker but instead attempted to control it and saw Parker chase away towards goal.
The big defender grabbed the striker leaving the referee with no choice but to show him a straight red card.
Parker hit the free-kick inches over the bar and there was also time for more controversy when Stephen McPhail appeared to stamp on Prendergast although on this occasion the referee showed only a yellow card.