Trevor Carson was the hero for 10-man Motherwell as Stephen Robinson's side battled through an uncomfortable clash with Coleraine.
Goals from Callum Lang and Tony Watt put The Steelmen in pole position in the first half, but two controversial penalties allowed Ken Doherty to level the game.
Bevis Mugabi was shown a straight red as the referee pointed to the spot for the second time with seconds left on the clock to allow Doherty to take the game to extra time.
However, it was Carson's heroics in the shoot-out that, saving three penalties, that secured a third round clash with Hapoel Be'er Sheva.
'Well started the game positively and caused havoc in the Northern Ireland box. A Liam Polworth corner found Mark O'Hara in the box after just five minutes and cleared the ball off the line by Stephen Carson.
Moments later Allan Campbell found Watt in space, and his driven shot was parried away by Gareth Deane, and no Steelman could cover the rebound.
Against the run of play, James McLaughlin got away from Ricki Lamie from a free-kick and somehow skewed the header wide from close range.
After a lucky escape, 'Well took the lead after 16 minutes a Stephen O'Donnell header from the edge of the box was latched on to by Lang. Deane made a good initial stop, but the forward converted the rebound.
A howler from the Coleraine keeper nearly opened the door for number two as he fumbled a O'Donnell thrown and Declan Gallagher chipped the ball towards goal.
However, the home side's Stephen O'Donnell cleared the ball off the line after 32 minutes.
The relentless visitors couldn't be denied a second before the break as a Lang cross fell to strike-parter Watt on the edge of the box and he hit the ball low and out of the reach of Deane after 36 minutes.
Just before the half-time break, 'Well were fired a warning shot as Lyndon Kane found McLaughlin again with a neat cross from the left but the striker blazed his header over the bar.
Just after half-time, an apparent off the ball pull by O'Hara saw the referee point to the spot and Doherty slotted the ball into the bottom corner.
There was a narrow escape for Stephen Robinson's side as Gareth McConaghie had the ball in the net after 59 minutes. However, moments later the linesman flagged Ben Doherty offside.
Glackin's free-kick found Stephen Lowry in space after 73 minutes as he beat Watt to the ball, but the ball was thumped over the bar from the centre of the box.
There was late heartbreak as Bevis Mugabi was judged to have pulled back Eoin Bradley in the 90th minutes, and Doherty calmly sent Carson the wrong way to level the tie.
With the game in extra time, fresh man Chris Long glided past the home defence and tried to beat Dean at his near post, but the shot bobbled wide of the near post.
There was a major let-off for the Fir Park outfit and so as Bradley met a neat cross with his head, and a fingertip save from Carson prevented the ball going over the line before it was booted clear.
In the shoot-out, Northern Ireland international Carson spared an Euro humiliation for his side by saving penalties from Parkhill, Kane and McConaghie for a 3-0 win.
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