England under-21 international goalkeeper Woodman denied Birmingham City's Lukas Jutkiewicz from 12 yards in the first half, standing up tall to block as the experienced frontman opted to go straight down the middle - a fifth save from the eight penalties he had faced since joining the Swans on loan from the Magpies at the beginning of last season.
Unfortunately for Woodman and the Welsh club, though, he couldn't keep out Scott Hogan when Lee Bowyer's men were awarded another spot-kick in the dying seconds, with the Blues coming away with a vital 1-0 victory.
Swansea stay third in the Sky Bet Championship, but missed out on the chance to close the gap on second-placed Watford following a third successive defeat.
Elsewhere on Friday, Kell Watts made his return from injury as he came from the bench in the 71st minute to help Plymouth Argyle beat AFC Wimbledon 1-0 in League One.
Lewis Cass played the full game as Hartlepool United made it 12 games unbeaten in the National League with a 2-1 home win against Dagenham & Redbridge.
And Elias Sørensen was a 74th-minute substitute as Almere City won 2-0 against NEC to strengthen their promotion challenge in the Eerste Divisie.