The Bluebirds boss watched his team stretch their unbeaten run to a dozen matches as they maintained a four-point lead over Lincoln, but extended the gap to 12 points between themselves and the play-off places.
Joel Colwill gave Cardiff the lead and although Matty Stevens drew Wimbledon level, second-half goals for Perry Ng, Ollie Tanner and Omari Kellyman underlined Cardiff’s superiority.
Such is Cardiff's firepower and confidence at present that even when they miss early opportunities, there is no panic or anxiety - just a firm belief that the next chance will soon be seized
“I knew the game wouldn't be straightforward and so I am very pleased to get the performance and result in the end,” said Barry-Murphy.
“I’ve had an uneasy feeling for the last couple of games and I knew how dangerous Wimbledon were and had seen how many goals they had scored recently.
“Our technique, in terms of how we crossed and passed the ball, needed to be improved and in the second half we did that and got the rewards we needed.
“We have depth and I think the players on the pitch, they feel the pressure of who's on the bench.”
It was a first defeat in four games for Wimbledon, who dropped one place to 16th in the table.
Wimbledon boss Johnnie Jackson felt his team had matched Cardiff in some areas, but could not compete with their firepower.
“It's strange. We've got beat 4-1 and I think there's loads to like from the team tonight,” said Jackson.
“I think we've caused them some problems, but obviously not enough. They're a top team, with top players and in the end, that was the difference.
“I think we've had 16 shots at goal, with six or seven to target, and we caused them problems at times.
“But they have got the quality to pick you off. We kept going for it, kept trying to commit bodies to the attack, and it left us a bit open and they had the quality on the night to take the margin up.”
Wimbledon had beaten the Bluebirds 5-1 in the Welsh capital in December, but that was in the EFL Trophy and was against a mainly second string home outfit.
The Bluebirds regular line-up had only lost once at home since - a 3-1 defeat to Chelsea in the Carabao Cup and they were dominant against a Wombles side that folded too easily under pressure.
Cardiff missed a few early chances, but there was no panic or anxiety before Colwill opened the scoring midway through the first-half.
Cardiff’s opening goal arrived in the 22nd minute when Colwill met Alex Robertson’s corner kick with a rising first-time strike inside the near post.
Wimbledon’s threat had been limited to a couple of eary half chances, but they managed to draw level in first-half stoppage time.
A free-kick by Steve Seddon found substitute Stevens, who slotted his volley neatly past Cardiff goalkeeper Nathan Trott.
Joel Bagan’s effort was deflected for a corner from which Cardiff regained the lead after 58 minutes.
Tanner’s delivery reached an unmarked Ng, whose header was too powerful for goalkeeper Nathan Bishop.
Wimbledon were in disarray defensively and went 3-1 behind three minutes later when Ng set up Tanner, who was allowed time to turn inside the box and fire home.
Kellyman buried his chance - and Wimbledon - when he was played in by substitute Callum Robinson in the 87th minute.
