On-loan Everton midfielder John Lundstram scored his first goal for the club in the 21st minute, rifling in from close range.
And the visitors' frustration boiled over in dramatic fashion in the closing stages with Kirk Broadfoot and Gary MacKenzie picking up second yellow cards either side of Ricardo Fuller's red for an attempted headbutt on Luke Ayling.
With the Glovers now just two points from safety and within five points of seven teams at the foot of the Sky Bet Championship, it meant a thoroughly pleasing night was capped by another positive for Johnson.
"That is another win for us and it is nice now to see four wins on the board and hopefully we can see some more quickly," he said.
"Psychologically to go above Barnsley and Sheffield Wednesday was massive and to beat Blackpool has dragged in probably seven or eight teams.
"All of a sudden you can pull in more teams than you could a few weeks ago and that is good.
"We knew Blackpool compete - that is why they are at the top end of the league.
"They compete and they have that little bit of quality and ability as well. They are all clever players so I am proud of our boys that we competed with them.
"We move on to the next game, which is a massive game against Charlton."