Rudy Gestede broke the deadlock after Chris Taylor had cancelled out Gylfi Sigurdsson's thunderbolt midway through the first half and another former Cardiff man, Craig Conway, added the third late on.
Blackburn were undoubtedly helped by Kyle Bartley's early sending off for bringing down the pacey Josh King as the last man, and Swansea ended the game with nine men after Sigurdsson jumped into a needless challenge on Taylor in injury time.
Bowyer said: "It's a good feeling. The lads are delighted. To beat a Premier League team and get through to the next round is terrific for us.
"It certainly levelled the game a bit for us when they lost the player but even down to 10 men they're a great team because of the manner in which they keep the ball."
Bowyer expressed his disappointment that fewer than 6,000 fans turned up, but added: "Hopefully we can get another home draw against a Premier League team and see if we can try and fill it."
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