They extended their lead thanks to Yeovil's failure to win at Doncaster in a lacklustre goalless game at the Keepmoat Stadium.
The Globers didn't land a single shot on target, but their defence was more than a match for a Rovers attack missing several key players.
Oldham's fourth defeat in a row left a massive hole in their automatic promotion bid and revived Blackpool's hopes of a play-off spot.
Andy Morrell scored the only goal of the game at Boundary Park as the Seasiders picked up their first win in seven.
The Latics hit the woodwork twice but the form which took them to the top of League One - they now trail table-topping Scunthorpe by 12 points - has faded.
Roberto Martinez's reign as Swansea boss got off to the perfect start thanks to goals from Pawel Abbott and Lee Trundle as the Swans ran out 2-0 winners at bottom club Rotherham.
Despite a blistering stoppage time free-kick from Martin Woods, Swansea were always in control and moved up to seventh in the table.
The future does not look as bright for the Millers, who are now winless in 14 games and appear cast adrift at the foot of the table.