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Oldham hit the woodwork twice but the form which took them to the top of League One has faded.
Blackpool defended well, with captain Michael Jackson outstanding at centre-half and goalkeeper Paul Rachubka - who once had a spell with Oldham on-loan from Manchester United - enjoying an impressive debut.
Oldham went close after only two minutes as 20-goal top-scorer Chris Porter met Andy Liddell's corner but gave Rachubka a comfortable save.
Paul Warne fired past the post from the edge of the box but chances were at a premium during the first half as defences stayed on top.
Blackpool appealed for a penalty on 32 minutes when Wes Hoolahan hit the deck under a tackle from Sean Gregan but there were no real complaints when the referee turned them down.
It was not until early in the second half that Blackpool created a chance, which midfield man David Fox headed over the bar from a right-wing cross by Simon Gillett.
Keith Southern hit a raking drive from 30 yards to test Oldham keeper Les Pogliacomi before the home side were thwarted by a combination of Rachubka and the woodwork.
Striker Warne was the frustrated man as his shot from just outside the box was touched against the bar before bouncing clear.
Rachubka also kept out Gregan before Blackpool made the breakthrough at the midway point of the half.
Ben Burgess seized on a misunderstanding in Oldham's defence and picked out Morrell, who was left with an easy task to find the unguarded net from three yards.
Blackpool could have doubled their lead through Adrian Forbes, who hit the post with an angled drive, or fellow substitute Keigan Parker, who missed the target from close range.
Oldham's frustration mounted in injury time when Porter hit a 22-yard free-kick against the bar with Rachubka beaten.