The Swans' best chance came from leading scorer Lee Trundle's 75th-minute free-kick, but he fired it just over the bar. The Welsh side's defeat means Southend United can go clear at the top if they avoid defeat against Nottingham Forest at Roots Hall today. A win for Steve Tilson's side will set a new Southend record of eight consecutive victories.
Elsewhere, the League One bottom side Swindon Town, another club in caretakership after Andy King's removal, went ahead against Port Vale thanks to Rory Fallon's seventh goal of the season midway through the first half. But a minute before the break Mickey Bell equalised for Vale, and eight minutes into the second period Chris Cornes scored Vale's second and it ended 2-1.
Just above Swindon, Gareths Edds' 72nd-minute strike gave Milton Keynes Dons the lead at Walsall, but Julian Bennett's injury-time equaliser earned the Saddlers a point. The 1-1 draw moved the Dons up two places.
In League Two, Leyton Orient missed the chance to go top after they were held to a 1-1 draw at lowly Stockport County. Tony Vaughan's goal midway through the first half gave County the lead but Gary Alexander's equaliser midway through the second half, his eighth goal of the season, earned the point that took Orient up to third. Stockport moved off the bottom.
The Nationwide Conference leaders, Grays Athletic, drew 1-1 at Woking, thanks to a calmly dispatched penalty by Stuart Thurgood.