Van Tornhout became an instant Kilmarnock legend when his late winner secured Killie the Scottish League Cup for the first time in the club's history.
The Belgian striker had replaced Gary Harkins in the 73rd minute and 10 minutes later he dramatically headed in a cross from fellow substitute Lee Johnson, who had come on for Danny Buijs early in the first half, to give the Ayrshire side a famous victory.
It was Killie's sixth attempt at winning the final and there were wild scenes of jubilation when the final whistle ended a dramatic afternoon at the national stadium.
Kilmarnock's win, helped by a great display by goalkeeper Cameron Bell, also scuppered Celtic's hopes of a treble - but it was a day for Ayrshire rather than Glasgow.
Both sides were in their changes strips but in familiar style, it was Celtic who started more confidently.
Captain Scott Brown drove wide of the target from distance with just over a minute played before an horrendous mistake by Killie defender Mo Sissoko in the fourth minute gifted the Parkhead side what would be the best chance of the half.
Under no pressure with the ball at his feet outside his own box, the big defender's sloppy pass across his back-line was intercepted by the lurking Gary Hooper
The Celtic striker had only Bell to beat but the Killie keeper made a good block to save the blushes of his lackadaisical team-mate.
Killie, tentative and nervous, slowly worked their way into the game.
Rugby Park midfielder Dean Shiels fired wide of Fraser Forster's left-hand post moments later but it took another Bell save in the 27th minute to keep the score level.
Brown skinned Killie midfielder Garry Hay on the right wing before crossing in for Anthony Stokes to bullet a header downwards, the Irishman looking in anguish as the Killie number one dived to push the ball away at his left-hand post.
At the other end, Celtic keeper Forster made a good save from Shiels' right-footed drive from the edge of the box and from the resultant corner, Stokes cleared Sissoko's header off the line.
It was an absorbing rather than an exciting contest but in the 39th minute Bell was called into action again when he tipped a powerful drive from the impressive Brown over the bar but the corner came to nothing.
It was becoming a tale of two keepers as Forster blocked an attempt by Killie striker Paul Heffernan just before the break, after a mistake by Celtic defender Kelvin Wilson had put the Parkhead side under pressure.
There was another early chance at the start of the second half, this time for Killie when Shiels burst into the Celtic box after getting the break of the ball.
The Northern Irishman had only Forster to beat but dreadfully mishit his shot from only six yards and ball spun wide of the target, turned back in by Rugby Park midfielder Jamie Fowler but to no avail.
The Ayrshire side enjoyed their first real concentrated spell of pressure and following a cleared Killie corner in the 54th minute Hay lobbed the ball back into the Celtic box but Sissoko, backpedalling, headed wide.
This was the cue for Neil Lennon to replace defender Thomas Rogne with midfielder Ki Sung-yueng, with Victor Wanyama moving back to defence and almost immediately the Hoops were back in control .
Just after the hour mark Celtic midfielder Joe Ledley fired wide of the target before Stokes, after making himself a yard of space inside the Killie, box shot straight at Bell.
The Kilmarnock keeper then tipped a Wanyama header over the bar following a Ki corner as the Ayrshire side's defending became increasingly desperate.
As extra-time began to loom, and legs became tired, Killie midfielder Liam Kelly fired just over the bar from the edge of the box.
Georgios Samaras replaced Hooper in the 79th minute but four minutes later Killie were dramatically ahead when Van Tornhout ran in at the back post to head Johnson's cross from the left past Forster.
The final minutes were fraught and here was time for Bell to make a double save, first from Samaras and then Kris Commons, who had come on for Ledley and for Stokes to get booked for simulation after Hoops appeals for a penalty came to nothing.
The final whistle, after four added minutes, brought roars from Killie fans whose club have now won all three major Scottish trophies.