The stalemate will move Cheltenham up to 22nd, above Rotherham, but still leaves them three points from safety.
Tranmere Rovers moved back into the play-off zone, they are now fifth, with their ninth home victory of the season over Crewe Alexandra.
They dominated proceedings at Prenton Park and could easily have won by a greater margin. The only goal came after 18 minutes,a s Gareth Taylor scored with an angled shot after Calvin Zola charged down a clearance from Julien Baudet.
Bristol City took a break from their League One promotion push to dump Championship side Coventry out of the FA Cup in a third round replay at the Ricoh Arena.
Gary Johnson's men had thrown away a 3-1 lead at Ashton Gate in the original tie, but they proved they were the better side over two games.
Scott Murray and Enoch Showunmi were the heroes of the night and the Robins could have won the game by a wider margin.
Oldham were unable to follow City's example, as Darren Potter's stunning strike put Wolves on course for victory in their tricky third round replay at Boundary Park.
The Latics may be flying high in League One, with a draw at Scunthorpe on Saturday keeping them in the hunt for automatic promotion, but the higher-division visitors brought them down to earth as Potter opened the scoring and Craig Davies made sure of the win.
The sides had drawn 2-2 at Molineux last week and Oldham again gave Wolves a scare by bossing the first half.
But top-scorer Chris Porter missed a great chance and Wolves eventually made their quality tell as they earned a mouthwatering fourth round clash against local rivals West Bromwich Albion.