Fabianski is set to get a chance to win over the critics tonight as Wenger rotates his team for the third-round clash at White Hart Lane
Fabianski - who conceded five goals on his last appearance at Tottenham in the Carling Cup semi-final two years ago - has stood in for Manuel Almunia at all levels since arriving from Legia Warsaw during May 2007.
Despite a number of high-profile errors - including in the 2009 FA Cup semi-final defeat to Chelsea on a birthday to forget at Wembley and also in the Champions League away to Porto last season - the young Pole continues to keep the faith of his manager.
"I am personally convinced he is a world-class goalkeeper, potentially, and of course when you have that potential you want to transfer that into competitive games," Wenger told Arsenal TV Online.
"I can only give him the opportunity to give him games to show what I believe about how good he is.
"I believe he has a very strong attitude, very strong response and he works very hard in training, so he has an opportunity to show his massive talent.
"I have massive faith in him and I think I have shown this historically. I am convinced he will become a great goalkeeper.
"We live in a world where if you have an opportunity you have to take it. You will get a second one, but you will not get 10 - and that is part of our job."
With Tottenham also now competing in the Champions League, Harry Redknapp will utilise his entire squad in an aim to protect player fitness.
As well as Fabianski, Johan Djourou, Emmanuel Eboue, Kieran Gibbs and Mexican striker Carlos Vela are all set to feature having been unused substitute at Sunderland, but the tie will also be an opportunity for youngsters like Jay Emmanuel-Thomas.
Wenger - who faces a possible touchline ban after being charged with misconduct by the Football Association following his reaction to Sunderland's stoppage-time equaliser at the Stadium of Light on Saturday - believes the 19-year-old forward has a bright future at Arsenal having picked up some valuable first-team experience last season during loan spells at Blackpool and Doncaster.
"Jay has class - class to give the ball, class to finish, class to pass people," Wenger declared.
"I believe he can play against anybody and score goals, but then again you must earn your place and on a daily basis he must show you have the hunger and quality.
"He has the needed quality without a doubt. I am confident that if he gets an opportunity he will show that."
Gunners skipper Cesc Fabregas, meanwhile, hopes he could recover from a hamstring problem picked up when scoring a freak goal at Sunderland in time for the Premier League trip to Chelsea on October 3.