Easter, who completed an emergency deadline-day loan move from MK Dons, will have done his chances of earning a coveted January switch to the Liberty Stadium no harm.
The Wales international's 27th-minute close-range finish from Nathan Dyer's cross proved the difference between the two sides and provided a much-needed victory for the Swans, who lost 4-0 at leaders QPR on Boxing Day.
They now head into 2011 in third place in the npower Championship, level on points with Cardiff and Leeds and with Norwich just one behind in what is rapidly becoming a thrilling promotion tussle.
It has been a disappointing Christmas period for Barnsley who have now lost both of their festive fixtures after a five-match unbeaten run and are down in 16th.
Stephen Dobbie tried his luck with just four minutes on the clock, drilling right of target from 18 yards.
And that set the pattern for an opening spell in which the hosts dominated proceedings - Dyer forcing a parried save from Tykes stopper Luke Steele during a period of play in which they enjoyed six corners in five minutes.
Adam Hammill forced a save from Dorus de Vries at the other end but that proved mere brief respite before the Swans broke the deadlock.
Dyer found enough space on the right side of the penalty area and picked out Easter from six yards who pounced to convert his first goal since August in what was only his first start for the Welsh club.
Both sides then exchanged chances - Hammill blasting off target for the visitors before Easter and Dobbie did the same.
Matchwinner Easter then came close to a second when he saw his header from 12 yards rebound off the bar.
The second half started with a chance for Barnsley after just 58 seconds, Jim O'Brien testing the reflexes of De Vries.
Dobbie continued to pose a threat for Swansea and it was he who almost grabbed the second goal the home side craved when Steele tipped his close-range shot around a post after 71 minutes.
It was De Vries' turn to next prove his worth, keeping out Goran Lovre's header and then Paul Hayes' drive as Mark Robins' charges pushed for an equaliser.
But despite their late pressure it was not to be, and it was Dyer who could have added a third for Rodgers' side but for another impressive stop from Steele.
That was before De Vries parried substitute Jacob Butterfield's 20-yard effort to safety in the fifth minute of injury time to ensure Swansea took the honours.