Manager Malky Mackay dropped striker Heidar Helguson in favour of 24-year-old Gestede who partnered Craig Bellamy while Aron Gunnarsson also came into the midfield.
And it was the former Metz forward who was quickest to repay the faith of his manager after just eight minutes when Craig Noone beat Shane Lowry with a mazy run before crossing for the Frenchman who tapped home from six yards.
The visitors' problems worsened 10 minutes later when winger Scott Malone had to be replaced by Liam Feeney with the Bluebirds already in a rampant mood.
Former Aston Villa defender Lowry made amends for his early lapse blocking a Bellamy effort inside the box while goalkeeper David Forde was forced to deal with a flurry of tricky deliveries in quick succession.
But they were showing no lack of firepower themselves following 11-goal Chris Wood's return to parent club West Brom. Lowry delivered for Darius Henderson on 24 minutes whose header drew a fine stop from David Marshall.
Substitute Mutch went close to a second 10 minutes after the restart but Forde produced a flying save to keep out his long range drive.
Dangerous in attack, the hosts looked susceptible at the back and Dany N'Guessan, recalled to the starting XI following the departure of Wood, fired a warning shot into the side netting on the hour mark after a swift counter attack.
Kenny Jackett's side were firmly on top in the second-half and the impressive Marshall was again called into action minutes later this time tipping Henry's free-kick round the post.
His opposite number was keen to prove his worth as the game began to open up in the final 20 minutes and Forde kept them in it with a brilliant parry to deny Noone.
Mackay introduced Helguson in place of Gestede 13 minutes from time as the Bluebirds used all their experience to hold on for a vital three points.