The Swans moved off the bottom of the division after a thrilling victory over promotion hopefuls Oxford.
"The game had passion, commitment, endeavour and good goals and on top of that it was a thrilling finish," said Swans manager Brian Flynn.
"We have proved we can come back from being a goal down but we were just starting to get on top when they broke away and opened the scoring." United took the lead in the 25th minute when Scott McNiven raced down the right flank and squared the ball to Andy Scott who beat Swans keeper Neil Cutler at his near post.
Nine minutes later Marc Richards fired in a shot which took a slight deflection before nestling in the bottom corner of the Oxford net.
The second half opened with the Swans netting twice in a four-minute spell with Lenny Johnrose heading home a precise Roberto Martinez cross and then Richards converting a penalty after Brad Maylett had been brought down.
Oxford put the emphasis on attack as the minutes passed by and Scott netted his second in the 82nd minute to set up a rousing finish.
"Leon Britton has fractured his cheekbone in that early clash of heads and will be out for the rest of the season and that will be a big blow for us," said Flynn.
"He has been outstanding for us and it will be a bitter blow not only for us but also for the young lad." Britton left the field as early as the seventh minute to be replaced by Gareth Phillips who slotted into his midfield position.
Double goalscorer Richards was delighted with his personal performance but also glad that his side had earned the win they so desperately needed.
"It was good to come back into the team after suspension and even better to score a couple of goals," he said.
"Originally Kevin Nugent was going to take any spot kicks but I grabbed the ball as I felt very confident.
"Since I came to the club I have had a stop-start time but now hopefully I can have a good run in the team and get some more goals to help the club move away from danger."