The Newcastle United stopper, who is on loan at the Liberty Stadium until the end of the season, started at Elland Road for Steve Cooper’s side.
The Swans’ winner came from former United man Wayne Routledge, whose low finish earned Woodman and his team – who are still unbeaten – the three points that saw them leapfrog their opponents at the top of the Championship.
Elsewhere in the Championship, Jacob Murphy came off the bench for the final quarter of an hour as Sheffield Wednesday sought an equaliser against Queens Park Rangers, but the 24-year-old couldn’t quite help Lee Bullen’s men pull a goal back as they suffered a 2-1 defeat at Hillsborough.
In League One, Dan Barlaser’s Rotherham United drew 1-1 at home to Tranmere Rovers, with the young midfielder substituted at half time.
And in League Two, Elias Sørensen made his first start for Carlisle United as they recorded a 1-0 win at Scunthorpe.
The frontman played the first 45 minutes before being replaced by Ryan Loft, who bagged the winner in the second half.
Grimsby Town ran out 3-1 winners at Walsall, with full back Liam Gibson entering the fray as a substitute for the Mariners with just over ten minutes left to play.
But Nathan Harker’s Blyth Spartans were beaten at the weekend, with hosts Leamington earning a 2-0 win in the National League North. Goalkeeper Harker was an unused substitute for Lee Clark’s men.
Photograph courtesy of Swansea City FC