Spanish international star Gaizka Mendieta scored the dramatic match-winning penalty after his man-of-the-match display in the Carling Cup.
It was fitting that Mendieta should be the hero after a highly impressive display.
Defences dominated in the 90 minutes and in extra time and it seemed inevitable that a penalty shoot-out would be required to settle the tie.
Middlesbrough manager Steve McClaren will obviously be happy with his side's Cup progress but, once again, his attacking limitations were exposed.
Massimo Maccarone made little impact in the 120 minutes while Michael Ricketts was equally ineffective after being introduced as a second-half substitute.
Wayne Rooney had a disappointing game for Everton and it was no surprise when the 18-year-old England star was called off in the first period of extra time.
At least, on this occasion, Rooney did not sulk after being withdrawn.
Middlesbrough kept another clean sheet in open play but their fans will be hoping to see more scoring power in future games.
For Everton there was not even the consolation of a Cup scalp after being sucked into the Premiership relegation dogfight.
Francis Jeffers had more goal attempts than any Everton player, especially in the first half, without any reward.
Just after the break Jeffers sent a header past the far post as Everton overran Middlesbrough's midfield and looked the more threatening.
When Le Tie was booked for a foul after 62 minutes there was an unnecessary bust-up among players before tempers cooled down.
Maccarone, who has yet to justify his £8million price tag, missed a good scoring chance to be Boro's match-winning hero in the closing minutes.
In the second period of extra time a Mendieta free-kick flashed inches past the far post while a match-winning chance by substitute Leon Osman was denied by Mark Schwarzer.
Osman was the only player who failed to hit the back of the net in the penalty shoot-out. To the cheers of the Middlesbrough fans behind the goal, his shot was saved by Schwarzer's legs.