Playing at home for the first time in 2018, the Hibs lost their first game since early November despite taking an early lead.
And what a strike it was as Garry Thomson claimed his 100th league goal for the club following good play from Raymond Crichton and Ben Anthony.
Tayport equalised in the 20th minute when Gary Sutherland smashed the ball home. Grant Paterson ought to have done better when he was presented with a great goal-scoring opportunity but he made amends in the 37th minute by sending in a deep cross that was perfect for the unmarked Sutherland to claim his and the visitors' second.
Shortly before half-time only a terrific goal-line clearance from Stuart Drummond prevented Sutherland from finding the net for the third time.
It was Dayle Robertson who eventually netted Tayport's third on the hour mark and although Andrew Adam did well to reduce the leeway in the 79th minute, there was no further scoring allowing Charlie King's side to go third equal in the league with Dunbar United.
GI Joinery Hibs' Man of the Match: Max Coleman
Thornton Hibs: Roberts, M.Robertson, McMillan, S.Drummond, Shields, Coleman, Keatings, A.Drummond, Anthony, Thomson, Crichton. Subs: Shanks, Adam, Lee, Ireland, McNab.
Tayport: Sorley, Conway, Rollo, Mackie, Gill, Sutherland, Robertson, O'Brien, McConnachie, Paterson, Anderson. Subs: Sturrock, Gray, Christie, Smith, Rennie.
Referee: Mr S.Gill
Match statistics:
Attempts at goal - TH 17 Ta 11
Attempts on target - TH 6 Ta 6
Corners - TH 3 Ta 3
Offside - TH 0 Ta 1
Fouls committed - TH 12 Ta 12
Yellow Cards - TH 2 Ta 1
Red Cards - TH 0 Ta 0