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The future does not look as bright for Rotherham, who are now winless in 14 games and appear cast adrift at the foot of the table.
Swansea swept into a 20th minute lead when Leon Britton fed Kevin Amankwaah down the right wing. His cross found Abbott unmarked at the back post and he had the simplest of tasks to head home.
Trundle and Andy Robinson both had chances to double the lead and Kristian O'Leary had a header blocked.
Rotherham forced a rare chance just before the break when Delroy Facey was played in down the left but he dragged his shot across goal.
Abbott curled a shot on goal as Swansea opened the second half looking to build on their lead.
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Moments later both Sharps and Craig Fleming combined to thwart both Robinson and Abbott.
Stephen Brogan lashed a fierce 25-yard drive wide as Rotherham toiled to get back into the game.
The second goal eventually came on 61 minutes when Swansea broke down a Rotherham free-kick in their own half.
Britton charged forward and played in Trundle, who cut inside and lashed a left-foot drive into the net from 18 yards.
Trundle almost had a second moments later when he was played through but Gary Montgomery saved.
Robinson then had a curling effort tipped away and Britton hit the post with the follow-up.
Willy Gueret had to make an excellent save to deny Woods in the closing stages and then in stoppage time Woods drove home a fierce consolation free-kick from 25 yards.