The first match played in the Welsh capital since the tragic death of Gary Speed was always going to be an emotional occasion, and the Cardiff City players dedicated this victory on Tuesday night to the manager who had put the pride back into his nation's football. Speed, lamented long, loud and with heartfelt feeling (the crowd chanted his name before, during and after the game) would have loved this, the team he knew so well deservedly beating Premier League opposition to claim their place in the semi-finals of the Carling Cup.

Kenny Miller's sixth goal of the season and a second from Filip Kiss added to the mounting misery of Blackburn Rovers' season, and well before the end their supporters were again calling for the dismissal of the embattled manager, Steve Kean.

Was he beginning to doubt his ability to transform a desperate situation? "No," he said. "It's never nice when people are being negative about you, but when the game starts I can put it to the back of my mind and it doesn't affect me." He remains confident that he will still be in charge for the match at home against Swansea City on Saturday, but faces another difficult meeting with the club's owners on Wednesday, having won only once in 13 league games this season.

They won this cup in Cardiff in 2002, beating Tottenham Hotspur in a final played at the Millennium Stadium, but this is a very different Rovers, odds on for relegation under Kean's increasingly unpopular management. The Indian owners are regarded more like cowboys, their absentee regime plunging a cheap and anything but cheerful team to the bottom of the table.

To the profound dismay and astonishment of the fans, Kean was "rewarded" with a pay rise last week. The defensive errors that have undermined Rovers all season betrayed them again after 19 minutes, when a poor touch from Morten Gamst Pedersen allowed Aron Gunnarsson to seize possession and bisect the central defenders with a perfectly weighted pass. Such situations are meat and drink to Miller, whose pace enabled him to break free and slot the ball through the goalkeeper's legs into the untenanted net.

It could easily have been 2-0 five minutes later, when Miller again evaded Mark Bunn, this time near the touchline on the left, before firing in a close‑range shot which Scott Dann blocked. Instead, Blackburn would have restored equality before half time but for the spectacular save with which Tom Heaton turned behind David Dunn's bristling 25-yarder.

Pressing for the security of a second goal, Cardiff got it five minutes into the second half, when Peter Whittingham's inswinging corner from the right was headed down at the far post by Anthony Gerrard and helped over the line by Kiss. Gerrard claimed it but the Cardiff manager, Malky Mackay, said: "I've seen the replay and Kiss chested it over the line."

Blackburn stirred themselves briefly, Grant Hanley threatening Heaton with a firm, downward header and David Goodwillie, the Scotland striker who chose to join Rovers in preference to Cardiff last summer, breaking through before he was thwarted by City's last‑ditch defence. But it was not happening for the visitors and, with an hour gone and their team on the way out, the Lancastrian fans vented their exasperation with choruses of "We want Kean out" and "You don't know what you're doing".

The manager responded by sending on Aiyegbeni Yakubu and Jason Roberts after 80 minutes but it was a classic case of too little, too late. Wage rise or not, he is living on borrowed time.