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The Robins hit the woodwork twice and were denied by on-loan keeper Joe Hart, who made two fine saves, before Southern swept in a shot from the edge of the area after Wes Hoolahan had found him in space with a pass from the left.
There was little between the teams in the first half although Blackpool took a goal lead into the break thanks to a well executed free-kick on 39 minutes.
Tricky wide player Hoolahan was tripped on the edge of the box by Cheltenham's Steven Gillespie, and left-back Robbie Williams curled a low left-footed shot around the defensive wall and just inside home keeper Scott Brown's right-hand post.
Earlier, Brown had saved well from a Keigan Parker sharp turn and shot, but the hosts also went close when captain John Finnigan volleyed just over the bar from 12 yards after a JJ Melligan corner had fallen for him.
Cheltenham drew level six minutes after the break when Gillespie was fouled in the area by Williams and Finnigan hammered the spot-kick past Hart.
The home side dominated the next 20 minutes or so with first Spencer and then Melligan hitting the woodwork.
Hart also dived to make saves from David Bird and Spencer, although Brown was forced to save his team with a fine block from Hoolahan at the other end.
With other results going against them it seems that Blackpool will have to be content with a place in the play-offs. Cheltenham, meanwhile, look a good bet to avoid the drop on this form.