The Croatian international netted the only goal in Bolton's fourth-round replay against Wigan on Wednesday night and his 19th-minute strike proved decisive again yesterday. It was the perfect end to a week when Klasnic, 30, saw an off-field nightmare brought to an end.
Klasnic was arrested in October after a 17-year-old claimed she had been attacked in a Manchester apartment, but all allegations were dropped this week.
Two in two: Ivan Klasnic (centre) celebrates the winner
Bolton boss Coyle said: 'We knew from the outset that he did nothing wrong. But the thing about it is in terms of his fan base in Germany and Croatia, a lot of people looked up to Ivan and it was horrible for them to read that, particularly when he was totally innocent.'
Fulham manager Mark Hughes, a four-time FA Cup winner with Manchester United and Chelsea, was left to lament an opportunity missed yesterday, particularly as his side were unbeaten at Craven Cottage in 2011 before yesterday's match.
The Welshman criticised referee Stuart Attwell after venting his frustration at an incident in first-half stoppage time. Gary Cahill and David Wheater muscled in on Moussa Dembele, pulling the Belgian's shirt, but Attwell let play continue.
On target: Klasnic scored in the first half with a 10-yard volley
But Bolton could point to missed opportunities, too. Kevin Davies was unlucky a push by Salcido in the area just after the re-start went unnoticed. Chris Baird might also have seen red and not yellow for shoving Martin Petrov. The Bulgarian responded and was also booked.
Hughes said: 'There were a couple of occasions where you want the referee to make a decision. You've got to be strong enough to make those decisions.'
MATCH FACTSFulham (4-4-2): Schwarzer 6, Baird 6,Hughes 5, Hangeland 6, Salcido 5; Gera 6 (Zamora 68min, 7), Sidwell 6, Murphy 6, Dempsey 7; Johnson 6, Dembele 7.Subs not used: Stockdale, Kelly, Pantsil,Kamara, Etuhu, Greening. Booked: Baird.
Bolton (4-4-2): Bogda 6; Robinson 6,Cahill 8, Wheater 7, Alonso 6; Lee 5,Muamba 6, Holden 6, Petrov 5; Klasnic 7(Elmander 79), Davies 7.Subs not used: Jaaskelainen, Taylor,Moreno, Blake, Cohen. Booked: Muamba, Petrov, Robinson, Holden.
Man of the match: Gary Cahill.
Referee: Stuart Attwell 3.
Attwell's apparent lack of control over this absorbing physical contest should not detract from Bolton's impressive performance.
Fulham's front two - Dembele and Andrew Johnson - certainly did not appreciate the close attentions of Cahill and Wheater, who were excellent. At the other end, Davies and Klasnic provided a constant threat.
Bolton, who will face Birmingham in the quarter-finals, were clinical where Fulham floundered. The hosts had seen Dembele scuff a left-foot shot and Johnson just missed a delightful ball from Zoltan Gera. But Klasnic pounced when Aaron Hughes and Brede Hangeland failed to clear Fabrice Muamba's cross.
Fulham were buoyed by the return of Bobby Zamora, making his first appearance as a 68th minute sub since breaking a leg on September 11.
But it was Bolton who had the best chance to seal the tie after 73 minutes when Davies found Petrov, unmarked, on the left side of the area but he failed to capitalise.
Coyle salutes Klasnic's character after Croatian striker nets winner in FA Cup tiePolice clear Bolton striker Klasnic of charges over alleged rape claimsAll the latest Bolton news, features and opinionAll the latest Fulham news, features and opinion
Explore more:People: Ivan Klasnic, Brede Hangeland, Kevin Davies, Mark Hughes, Fabrice Muamba, Gary Cahill, Andrew Johnson, Bobby Zamora, Martin Petrov, David Wheater, Owen Coyle, Stuart Attwell Places: Birmingham, Manchester, Germany, Croatia