The 24-year-old shot-stopper made a string of excellent saves to deny Spurs until the 74th minute, when Ryan Nelsen nodded home Rafael van der Vaart’s corner to finally put the home side ahead.
Gareth Bale then added a second for Tottenham with a neat finish, and Louis Saha secured victory with a splendid strike, ending any hope of Bolton comeback after Kevin Davies had cut Spurs’ advantage to one goal.
“It was a good performance,” the Spurs boss told ESPN. “We played with three in midfield and three forwards which suited us. We dominated the game but couldn’t get the goal.
“The keeper was amazing for Bolton. I’ve never seen a keeper make so many saves. He made save after save, and we hit the woodwork.
“We had an incredible amount of chances we just couldn’t get the break in front of goal.”
After a frustrating first half with Bogdan producing a series of top saves to deny Bale and Van der Vaart, Spurs finally made the breakthrough when Nelsen netted his first goal since moving to north London.
With Bolton pressing for an equaliser, Tottenham substitute Jermain Defoe launched a counter-attack, finding Bale with an incisive pass – and the Welsh midfielder curled his shot past Bogdan.
Bolton boss Owen Coyle introduced Davies in the final 10 minutes and the veteran striker scored from close range in the 90th minute to give the visitors late hope.
But any chance of a stirring comeback was eliminated when Saha’s powerful shot soared high into Bogdan’s right corner to set up a semi-final tie against Chelsea at Wembley.
“We’re disappointed to lose the game,” said Coyle afterwards. “We can’t argue that Tottenham Hotspur were the better side over the duration of the game.
“For the players to go out and show the spirit they did, even at 2-0 down, we could have felt sorry for ourselves, but we kept going because we’re very much a group.”
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