The Amsterdam side picked up a comfortable lead before the break, but Twente fought back in the remainder of the game and Janko eventually helped his side to KNVB Beker glory
Ajax scored twice before the interval via Demy de Zeeuw and Lorenzo Ebecilio before Wout Brama pegged one back in the dying minutes of the first half. Twente started the second half superbly and deservedly leveled the score via Theo Janssen. Both sides got a number of chances to decide the game in regular time, but failed to find the net a third time, sending the match into extra time. Marc Janko then netted the winner in the closing stages of extra time to help Twente to KNVB Beker glory.
Both sides started the match with attacking intentions, but it was Ajax which first came close to breaking the deadlock. Demy de Zeeuw spotted that the Twente goalkeeper was off his line and tried his luck from 50 yards out, only to see his shot sail just over Sander Boschker's goal.
De Zeeuw had more luck after about 20 minutes though. Siem de Jong set up the Netherlands international with a low pass on the edge of the area and De Zeeuw went past Theo Janssen before slotting home from inside the area.
Twente wasn't impressed too much and should have leveled the score only minutes later. Janssen reached Luuk de Jong with a superb free kick, but the young attacker aimed just wide of the Ajax goal.
This mess proved to be pretty costly later in the first half as Lorenzo Ebecilio doubled Ajax's lead with a deflected shot from the edge of the area.
The Godenzonen then escaped when Bryan Ruiz fired just wide after a superb cross from the left, but holding midfielder Wout Brama did peg one back in the dying minutes of the first half with a calm finish after being set up by Luuk de Jong.
The Tukkers started the second half brilliantly and got several chances to restore parity. Nevertheless, Vermeer showed why he is so highly rated in Amsterdam and surroundings as he made some excellent saves to deny Chadli and Denny Landzaat.
However, Vermeer was left without a chance after 55 minutes of play when Janssen found the net from the edge of the box. Luuk de Jong made the goal with a superb individual action down the left before laying the ball off for Janssen, who coolly slotted home.
Twente continued to dominate after the break, but Ajax almost grabbed the lead again around the hour mark. The Tukkers allowed young winger Ebecilio too much space down the right and the Holland under-21 star beat the Twente goalkeeper with a powerful shot, only to see his shot bounce back off the upright.
The Tukkers got a huge chance to decide the match with five more minutes to go. Brama set up Chadli with a good cross inside the area and the winger then headed the ball toward Ruiz. The Costa Rica star beat Vermeer to the ball, but aimed inches wide of the Ajax goal.
Luuk de Jong then came close in the dying seconds of the game with a good header after a cross from the right, but his attempt went inches wide at the far post.
Ajax started extra time superbly and almost grabbed the lead in the 96th minute. Vurnon Anita set up substitute Daley Blind with a good cross from the right and the full-back's header beat Boschker, only to hit the upright before going out for a goal kick. The Godenzonen again came close minutes later via Siem de Jong, but his low shot was saved by Boschker.
Bart Buysse got the best chance for Twente in the second half of extra time, but the Belgian fullback was denied by yet another outstanding save from Vermeer. The Eredivisie champions got their third goal of the game after 117th minutes though. Janssen sent in a superb free kick for Marc Janko and the towering forward beat Alderweireld to the ball before heading home.
Ajax and Twente will meet again in the Amsterdam ArenA on May 15 in what will be the decisive game of this year's Eredivisie.
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