Evra put United in front after 16 minutes at the Liberty Stadium with a glancing header from Robin van Persie's inswinging corner. The Frenchman, who joined United in 2006, has doubled his club haul in one half of a season - and it's all down to confidence.
"It's not an accident," he told MUTV. "I've started to believe that I can score. That's why whenever we get a corner kick I try to put myself in the right place. It's always a good delivery too - Wayne [Rooney] has set up two of my goals, and today it was van Persie."
The elation was short-lived, however, as Michu equalised for Swansea after 29 minutes and the Reds endured a second-half filled with frustration as attempts on goal hit the woodwork or white shirts.
"The most important thing was trying to win the three points," added Evra. "So we are disappointed. I think we deserved to win; we created so many chances and yet in the end we go back to Manchester with only one point. We're disappointed with the result, but not the performance."