Abou Diaby and Eduardo da Silva put the Gunners 2-0 ahead inside 30 minutes but a goal either side of the interval from Roque Santa Cruz, who scored a hat-trick on Saturday, sent the game into extra time.
Arsenal were made to play the extra half an hour with 10 men after Denilson was dismissed just before the end of normal time but Eduardo's second of the night after 103 minutes sealed their progress.
Wenger, who confirmed he will continue to pick his emerging players in the remainder of the league cup competition, told Sky Sports: "We want to finish the job we started last year.
"We have a good opportunity now - in the semi-finals."
The Gunners are at that stage for the third successive season, having lost to Chelsea in last season's final - and Wenger is starting to think they have it in them to go one better.
"This was a big test. They [Blackburn] came back to 2-2 and were very committed," he said, reflecting on a match in which Roque Santa Cruz scored the two home goals and Arsenal had to play extra time with 10 men after Denilson was sent off for a foul on David Dunn.
"When our football was not speaking any more we had to do something else - and we found the resources to score a third goal with 10 men, which is really promising for such young players," Wenger added.