It took penalty kicks to finally separate the teams in this third round Fife and Lothians Cup-tie.
The Capital side went ahead in the 41st minute when Christopher Hendrie sent in a free-kick to the back post that Taylor Hendry headed home.
This lead lasted just a few minutes before Raymond Crichton converted Max Coleman's corner-kick to level the tie.
Ten minutes into the second-half, Hibs' midfielder, Adam Drummond, smashed the ball home via the underside of the crossbar but by the 72nd minute it was all-square again when Taylor Hendry went on a strong run then shot low into the net.
There was no further scoring in normal time meaning that the tie went to a penalty shoot-out. In total, nine penalties were taken with the unfortunate Daryl Johnson missing United's second spot-kick leaving the Hibs to progress into the quarter-finals where they'll play host to either Glenrothes or Newtongrange Star.
SM Electrical Services Hibs' Man of the Match: Dean McMillan
Edinburgh United: Newman, Subasic, McAleavy, Conlon, Hendry, Johnson, Conaghan, Auriemma, Hendrie, McKinlay, Flynn. Subs: Lee, Murray, Hanratty.
Thornton Hibs: Roberts, M.Robertson, McMillan, S.Drummond, Shanks, Coleman, A.Drummond, Hepburn, Ireland, Thomson, Crichton. Subs: McNab, D.Robertson, Dursley, Burns.
Referee: Mr D.Graves
Match statistics:
Attempts at goal - EU 7 TH 7
Attempts on target - EU 6 TH 3
Corners - EU 3 TH 3
Offside - EU 1 TH 3
Fouls committed - EU 12 TH 17
Yellow Cards - EU 1 TH 2
Red Cards - EU 0 TH 0