Maresca’s side took the lead thanks to Alejandro Garnacho’s strike early in the second half of the quarter-final in the Welsh capital.
Chelsea were pushed hard by the gritty League One leaders, who equalised through David Turnbull’s thumping header.
But the Blues delivered a welcome tonic for Maresca after his recent outburst, as Pedro Neto and Garnacho struck in the closing stages.
When Maresca faced the media on Monday, the Italian refused to clarify his explosive claim after Saturday’s 2-0 win over Everton that the previous 48 hours had been his worst at Stamford Bridge because he and his team lacked “support” from “many people”.
Maresca’s rant had fuelled speculation he was criticising the club’s co-owners Todd Boehly and Behdad Eghbali and sporting directors Laurence Stewart and Paul Winstanley.
It has been suggested that Maresca was unhappy with the failure of Chelsea’s hierarchy to publicly support him amid criticism of his rotation policy during the team’s recent dip in form.
The victory over Cardiff was only their second in six games in all competitions.
Maresca, who led the Blues to Club World Cup and Uefa Conference League glory earlier this year, has now led Chelsea to three semi-finals in 18 months.
Asked if he felt backed by the club, Maresca said: “Tonight the focus has to be that we reached the semi-final, the support from fans has always been there.”
“We are going in the right direction, everything I do is because I want the best for everyone, the fans, players everyone,” he said.
“Very happy, especially for the effort of the players. I said yesterday that the schedule is full of these tricky games and so you have to pay attention and we did that.” (AFP)