A penalty from Tim Hicks five minutes from time looked to have earned Carmarthen Town a point against their west Wales rivals, but Jarman broke their hearts in the third minute of stoppage time, after Chris Venables had given the Reds a 72nd-minute lead.
Rhyl remain in third after being held to a goal-less draw at near neighbours Prestatyn in front of Boxing Day's highest crowd of 762. The Lillies played all of the second-half without striker Lee Hunt, who was dismissed four minutes before the break.
But Aberystwyth moved into fourth place after Luke Sherbon and Glyndwr Hughes headers had given them an early two-goal lead at home to Haverfordwest County. The Bluebirds' cause was not helped by a red card for Bobby Briers and, although Jack Christopher pulled back a late consolation from the penalty spot after Steff Williams had been felled, the visitors slipped to a 2-1 defeat.
Airbus UK Broughton failed to turn their domination into goals after Marc Lloyd Williams had headed them into a seventh-minute lead at home to Elements Cefn Druids.
And they paid the price in the 85th-minute, when sub Gary Penlington notched an equaliser for the lowly Ancients in a 1-1 draw at The Airfield.
Despite being without three suspended regulars, John Toner's 12th-minute effort was enough to hand all three points to Bala Town in a victory at Gap Connah's Quay.
The day's other two games, Caersws v Newtown and Welshpool v TNS, were postponed due to frozen pitches.