Gort never led but got away with hitting eight wides in the second-half when Aidan Harte struck the equaliser from a 65 in the third minute of added time.
Gerry Quinn had earlier hit seven points from dead balls, but missed two late on, while Harte showed admirable nerve to land his first point of the day and send the game to a replay.
Played in sheeting rain and howling wind throughout, St Thomas got off to a great start when Richie Murray struck a terrific point after three minutes before Conor Cooney soon doubled their advantage.
Quinn landed a pair of frees to draw Gort level after 12 minutes, but three points from St Thomas – two frees from Conor Cooney and a David Burke score – gave the Kilchreest men a three point cushion.
St Thomas held a 0-6 to 0-3 lead at the break and managed to pull four clear after the restart via Cooney.
But with the wind at their backs Gort were the superior team in the second-half and Paul Killilea’s point was quickly followed by a 65 from Quinn to push Conor O’Donovan’s side back to within two points.
James Regan pointed for Thomas’ after a great move involving David Burke and Richie Murray in the 42nd minute, but from then on Gort took control.
A needless foul on Richie Cummins gave Quinn the first of two frees in two minutes, but Cooney’s fifth point nine minutes from time looked to have settled St Thomas.
Quinn reduced the deficit to a point in the 55th minute, but two minutes later he looked to have passed up the chance of a draw when he mis-hit a 65.
But deep into added time, Harte took on the responsibility and landed a 65 to earn Gort a replay.
Scorers for Gort: G Quinn 0-7 (6fs, ‘65), P Killilea 0-1, A Harte 0-1’65
Scorers for St Thomas: C Cooney 0-5 (4fs), R Murray 0-2, J Regan 0-1, David Burke 0-1.
GORT: P Cummins; C Helebert, M McMahon, M Cummins; J Grealish, S Óg Linnane, B Regan; G Quinn, A Harte; K Killilea, P Killilea, G Lally; G O’Donoghue, O Fahy, R Cummins.
Subs: A Mullins for K Killilea (44).
ST THOMAS: P Skehill; C Burke, Robert Murray, S Skehill; E Tannion, Darragh Burke, S Burke; K Burke, David Burke; G Murray, B Burke, Richie Murray; C Cooney, A Kelly, J Regan.
Subs: S Cooney for G Murray (h-t), E Burke for Kelly (52).
Referee: John Keane.