Although Thornton's Garry Thomson saw an 11th minute header cleared off the line by Grant Paterson, Tayport could've been out of sight by the interval but for some slack finishing by Dayle Robertson, Jamie Gill and Conor Ireland.
The second-half was more evenly contested and it was Ben Anthony who gave the Hibs a 56th minute lead after being set up by half-time substitute, Chris Ireland.
In the 78th minute, Gavin Sorley made a brilliant save to prevent Garry Thomson from doubling the visitors' advantage and this was crucial because the ball was immediately worked to the other end where Dayle Robertson finished in style.
Sorley made another fine save to keep Adam Drummond's equally impressive header out but the save of the day was by Ryan Linton who, in stoppage time, somehow tipped Dale Reid's powerful drive on to the roof of the net to ensure that the Hibs extended their unbeaten run to ten games.
SM Electrical Services Hibs' Man of the Match: Ian Hepburn
Tayport: Sorley, Conway, Rollo, Gray, Gill, Ireland, Robertson, O'Brien, Tulleth, Paterson, Suttie. Subs: Reid, Sutherland, Christie, Rennie, Anderson.
Thornton Hibs: Linton, Crichton, M.Robertson, S.Drummond, Shields, Coleman (Ireland), Keatings, Hepburn, Anthony, Thomson, A.Drummond. Subs: Ireland, Shanks, Watson, Mackie, Simpson.
Referee: Mr B. Dickson
Match statistics:
Attempts at goal - Ta 12 TH 10
Attempts on target - Ta 5 TH 5
Corners - Ta 7 TH 5
Offside - Ta 3 TH 1
Fouls committed - Ta 15 TH 14
Yellow Cards - Ta 2 TH 5
Red Cards - Ta 0 TH 0