Despite taking a two goal lead, Thornton exited the East of Scotland Cup at the first hurdle with goalkeeper, James Penman, being the home side's hero with a number of great saves including the crucial one from Garry Thomson in the penalty shoot-out.
It was Thomson who gave the Hibs an 8th minute lead with a fierce drive from outside the area and they came close to doubling this lead shortly after only for Penman to deny Liam Forbes. Penman then made a terrific save to prevent Shaun Keatings' equally impressive 20-yard volley from counting.
The Whitburn 'keeper was powerless though to prevent Keatings from netting from the spot in the 36th minute, after Connor McQueenie was rather harshly judged to have handled the ball despite having his back turned when Thomson shot for goal.
A great save by Ryan Linton from Dewi Taylor shortly before half-time showed that Penman didn't have the monopoly on good stops but there was still time for the home side's number one to deny Matthew Robertson with another great save before the referee called a halt to first-half proceedings.
Whitburn were vastly improved in the second-half and pulled one back in the 63rd minute when Jack Hamilton slotted home. The Hibs replied through Thomson who watched in disbelief as Penman tipped his ferocious drive over the top for a fruitless corner-kick.
Forbes had the ball in the net in the 69th minute but it was chalked off for offside, a decision that baffled the visitors.
Gary Brass equalised in the 82nd minute when he rounded Linton then stroked the ball into the unguarded net.
With the game remaining all square when the full-time whistle went, the tie went straight to pens with the home side eventually coming out on top.
SM Electrical Services Hibs' Man of the Match: Matthew Robertson
Whitburn: Penman, Runciman, McQueenie, G.Hamilton, Greig, J.Hamilton, Patrick, Taylor, Brass, Thomson, Tomaszewski. Subs: Graham, Martin, Chisolm, Wilson, Allan.
Thornton Hibs: Linton, D.Robertson, M.Robertson, S.Drummond, A.Drummond, Coleman, Keatings, Crichton, Forbes, Thomson, Feeley. Subs: Taylor, Burns, Dursley.
Referee: Mr C.Newman