Middlesbrough poured more misery on struggling Everton, knocking them out of the Carling Cup in the third round.
A series of fine saves from Nigel Martyn denied Mark Viduka and James Morrison as Boro pressed forward.
But Jimmy Floyd Hasselbaink made Boro's pressure count when he latched onto Viduka's through-ball from 10 yards.
James Beattie nearly equalised with an acute shot but neither he, or debutant Andy van der Meyde, could break down the 2004 winners who held on.
Teenage midfielder Morrison was at the thick of things for Middlesbrough right from the whistle.
The 19-year-old forced Martyn to save at his feet before sending another effort from the edge of the box just wide.
Spanish midfielder Mikel Arteta was equally influential for Everton and was unlucky to see his six-yard shot blocked.
But as the pulsating half continued, it was Middlesbrough who eventually began to gain the upper hand.
Martyn kept Boro at bay, impressively saving shots from both Emanuel Pogatetz and Viduka.
The veteran keeper was eventually caught out by Hasselbaink's low shot through his legs seven minutes before half-time.
James Beattie almost grabbed a quick equaliser after the restart, his angled strike forcing Mark Schwarzer to make a tricky save.
Just after the hour, Van der Meyde was handed his first start for the club in place of James McFadden and he produced some excellent curling crosses into the box.
But it was Steve McCLaren's side who continued to pose problems for Everton's slow-footed defence on the counter-attack.
Hasselbaink saw his stinging shot hit the bar before clipping another shot narrowly wide.
In the dying minutes of the match, Arteta was denied at the other end when his 20-yard free-kick smashed the cross bar.
It was just not Everton's night - and Middlesbrough marched into the last 16.
Middlesbrough boss Steve McClaren:
"I asked them for character after what happened on Sunday at West Ham, and that's what I got.
"Our attitude was spot on and were determined. We broke well, made loads of chances and dominated in midfield.
"We have learned to defend well to keep leads, like we did last week in Europe against Grasshoppers."
Everton boss David Moyes:
"We are very disappointed not to have gone through, and that we didn't get a better result.
"We were disappointed we didn't make more of the crosses. We got a lot into the box but Boro defended well.
"We didn't get on the end of enough of our opportunities. We improved after the break but we couldn't get that elusive goal."
Everton: Martyn, Hibbert, Yobo, Weir, Ferrari (Bent 41), Arteta, Neville, Davies (Osman 78), Kilbane, McFadden (Van der Meyde 62), Beattie.
Subs Not Used: Wright, Kroldrup.
Middlesbrough: Schwarzer, Queudrue, Riggott, Ehiogu (Bates 45), Parnaby, Rochemback, Morrison, Pogatetz, Doriva, Hasselbaink (Nemeth 67), Viduka (Yakubu 78).
Subs Not Used: Jones, Kennedy.
Booked: Rochemback, Viduka.
Goals: Hasselbaink 38.
Ref: P Walton (Northamptonshire).