Jim Jefferies side had Marian Kello to thank for another hugely impressive display against the Champions who played well but lacked a killer touch in front of goal.
In the end Stevenson provided it for the Jambos when he fired the ball home from close range with just thirteen minutes left of what was a remarkable SPL encounter.
After just 60 seconds the game burst in to life when a turn and shot from Lafferty brought out a good save from Kello who dived low to his right.
At the other end Hearts showed their attacking threat when Eggert Jonsson passed the ball inside and Stevenson’s shot curled over Allan McGregor’s bar and in to the packed away end of the ground.
It was relentless stuff and it was a miracle that the Jambos survived an early onslaught.
With eight minutes played Kello held a sclaffed Lafferty shot after Mo Edu had created the chance with a clever cut back.
The energetic Steven Naismith then tried his luck with an audacious curling shot from a wide position which went a foot wide of the Slovakian’s far post.
With Rangers pushing forward at will Ness then decided to advance.
On 14 minutes Naismith found the 19-year-old as he made an overlapping run and his near post shot was parried away by Hearts’ busy keeper who then had to produce a world class stop to deny Ness yet again.
The Murray Park kid smashed a left-foot drive towards the postage stamp from 25 yards but the impressive shotstopper made a wonderful fingertip stop.
Remarkably, the pressure never stopped.
On 22 minutes Edu released Lafferty and the Ulsterman elected to shoot from 25 yards but Kello gathered the ball confidently.
With the game opening up and the tackles flying in it was only a matter of time before the ref pulled out his notebook and first to see yellow was Lee McCulloch for a challenge on David Templeton.
Lee Wallace was next before Madjid Bougherra was also harshly booked after questioning a poor decision from the official.
With a minute of the half remaining a hopeful punt up the park by Jonsson almost caught out McGregor with the ball bouncing over the Gers’ no 1 who managed to touch the ball in to the side netting.
Despite an impressive 45 minutes display from Rangers the scoreline was goalless at the break, mainly due to the performance of Kello.
The big question was whether they could maintain the tempo set in the first-half and in the opening five minutes of the restart they did with Edu edging closer to Lafferty in the last third.
On 51 minutes Papac did well to win a corner and when Davis swung in a deep cross Weir headed over from 15 yards.
And in the very next attack Papac drifted past three Hearts players but his right foot shot went straight in to Kello’s arms.
With his side struggling to retain possession Jim Jefferies changed his system to 4-4-2 with David Templeton, who had been brilliantly marked out of the game by Whittaker, being replaced by Gary Glen who joined Stevenson in attack.
On the hour mark Lafferty was brought down 25 yards from goals and despite scoring from exactly the same spot on October 2, he let Steven Davis take the free-kick but his effort hit the defensive wall.
With 20 minutes left the Rangers fans were out of their seats as Nikica Jelavic was introduced to the game in place of Lafferty and it was not long before John Fleck was also given a run-out with Edu taken off.
But against the run of play Hearts stunned their Glasgow opponents by taking a shock lead.
A cross came in from the left and with the Rangers defence unable to clear the ball Stevenson was there to prod the ball home with McGregor grounded.
Smith’s troops were stunned but with the just five minutes remaining an acrobatic effort from Jelavic smashed off the underside of the bar before bouncing on the line.
The ball was cleared to safety and this was to be the last chance of the match for the Rangers players who will be deeply frustrated to lose in the capital having put so much effort in to this dramatic 90 minutes.