Guthrie scores on debut
The Cottagers had earlier taken Bolton to extra time when substitute David Healy struck twelve minutes from time after Wanderers had taken the lead through Danny Guthrie on his debut.
Giannakopoulos, making his first appearance of the season, struck his first Bolton goal since March 2006 when putting the Trotters into the lead in West London and this ultimately secured their progression into the next round.
Bolton had made nine changes from the side which held Tottenham Hotspur to a 1-1 draw at the Reebok Stadium on Sunday whilst Fulham made a few changes from their line up which competed in the thrilling 3-3 draw against Manchester City.
In truth the Wanderers deserved their win and Norwegian international Daniel Braaten could have and should have gotten on the scoresheet in what was his first Bolton start since making the move from Rosenberg.
Braaten squandered his first chance of the evening after just seven minutes when Mikel Alonso's free kick was gathered comfortably by Fulham's veteran goalkeeper Kasey Keller.
Hameur Bouazza tested the Bolton goal a couple of minutes later but the former Watford midfielder saw his free kick gathered comfortably by Wanderers keeper Ali Al-Habsi.
Al-Habsi, signed from Norwegian outfit Lyn Oslo in January 2006, was making his first ever Bolton appearance and the Oman international did well in deputising for Jussi Jaaskelainen.
Christian Wilhelmsson and Mikel Alonso then had half chances for Bolton but defender Abdoulaye Meite came the closest and nearly netted his second goal of the week when firing just over the Fulham crossbar.
Bolton should have taken the lead on 23 minutes through Braaten but the summer signing could not find a way past Keller following Alonso's corner.
The Scandanavian should have given the Wanderers the lead shortly before the half hour mark but the former Millwall, Leicester and Tottenham goalkeeper Keller saved the ball with his chest.
On the stroke of half time Braaten again should have put Bolton in front but this time the legs of Keller saved Fulham from going one goal down.
Shortly after the break Bolton bossed the play with the recalled Gavin McCann firing high and wide from distance but what was to come next will live long in the memory for one young man who is just starting out in football.
Midfielder Danny Guthrie, celebrating his first start since moving on loan to Bolton from Liverpool earlier in the season, smashed home a superb right foot strike on the volley which left the experienced Keller gasping for air.
In putting Bolton in front in the 57th minute the 20 year old England youth star Guthrie netted his first goal at senior level and what a strike it was.
With just over 20 minutes of the game to go Bolton's goalkeeper Ali Al-Habsi made a good save to deny Fulham's charasmatic American front man Clint Dempsey and moments after Wanderers winger Christian Wilhelmsson saw his shot sail aimlessly over.
The introduction of Northern Ireland attacker David Healy boosted Fulham and the former Manchester United trainee put the London side back on level terms with just over ten minutes of the game to go when firing a shot through a crowded penalty area past Al-Habsi to take the game into extra time.
Healy hit the bar ten minutes into extra time but Bolton had defender Abdoulaye Meite to thank for clearing the scraps on the rebound.
Indeed it was Meite who proved to be a threat at the other end of the field but the Ivorian had an effort ruled out in extra time due to the officials declaring offside.
Bolton's last hope was to introduce their veteran Stelios Giannakopoulos for his first action of the new campaign and the Greece international responded by netting the winner from close range with eight minutes of extra time to go.
Al-Habsi kept out Fulham sub Diomansy Kamara in the later stages but Bolton held on for what is only their second win of the campaign so far.
Bolton will now go into the hat for the next round ahead of their important weekend tie away at fellow strugglers Derby County on Saturday.
BOLTON WANDERERS: Ali Al-Habsi, Nicky Hunt, Abdoulaye Meite, Lubomir Michalik. Gerald Cid, Danny Guthrie (Andranik Teimourian), Gavin McCann, Mikel Alonso, Christian Wilhelmsson, Daniel Braaten (Stelios Giannakopoulos), Kevin Davies
SUBS NOT USED: Kevin Nolan, Ricardo Gardner, Ian Walker (GK)
FULHAM: Kasey Keller, Chris Baird (David Healy), Aaron Hughes, Carlos Bocanegra, Paul Konchesky, Seol Ki-Hyeon, Steven Davies, Danny Murphy, Simon Davies, Hameur Bouazza (Diomansy Kamara), Clint Dempsey
SUBS NOT USED: Dejan Stefanovic, Alexei Smertin, Tony Warner (GK)
ATTENDANCE:
10,500
REFEREE:
Steve Bennett
BOOKED:
Baird (Fulham)
Murphy (Fulham)
McCann (Bolton)
Davies (Bolton)
Cid (Bolton)
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