Stallard left Meadow Lane for Barnsley in January 2004 and returned on loan a month ago, this being his sixth appearance - and his first goal.
Ironically, Stallard almost did not play because of flu and confessed that when brought off by player-manager Ian Richardson five minutes from the finish he was all in.
The first half was disappointing in difficult playing conditions with sleet, snow and sunshine alternating to pose problems for the players.
The second half was by far the better of the two and became much more open once Notts had broken the deadlock.
Stallard's strike from the edge of the penalty area followed one of the best moves of the match in which Robert Ullathorne and David Pipe combined to open the Swans defence.
Stallard immediately raced to the popular side to receive the acclaim of the fans though admitting afterwards he should first have gone to Pipe for creating such an excellent opportunity.
Fellow striker Glynn Hurst, so out of scoring touch recently, had a great chance to double Notts' advantage with an hour played but his effort was blocked on the line and Paul Bolland fired the rebound into the crowd.
It was a pity that Bolland, County's outstanding player, did not manage to add a goal to his midfield graft.
County lost their captain and central defender Julien Baudet to a calf strain after only 15 minutes. He was replaced by 19-year-old Emmet Friars who joined 19-year-old Kelvin Wilson and 18-year-old Shane McFaul and the three youngsters did superbly well as Notts kept a clean sheet.
Behind them Saul Deeney was called upon to make just one fantastic one-handed save to deny Izzy Iriekpen who must still be wondering how he failed to find the equaliser.
In the end Notts deserved to finish a poor run at home which had seen them draw twice and lose twice and they are now overall unbeaten in a run of five - the season's best.