Few could argue we were the better side for the first 68 minutes - Roy Carroll made some key saves, Derby had one big chance missed by Giles Barnes - but Robbie Keane's opener, a tap in after Steed Malbranque's shot was parried, appeared to sink the Rams while we grew stronger and stronger.
Younes Kaboul fired in the second after Pascal Chimbonda nodded Aaron Lennon's corner into his direction and substitute Dimitar Berbatov capped a hugely-impressive cameo performance off the bench with a penalty in injury time.
"Football games last for 90 minutes so I think you must look at the overall picture," reflected Juande.
"I think that Derby worked so hard for the first hour that the effort they used started to tell in the last 30 minutes and that is where we were able to make use of it."
Juande insisted it was a game he was determined to win when he brought Berba into the action. "It was 0-0 and we wanted three points, it was always an important three points for us," he said.
"Sure, he played his part in the team's magnificent effort in winning the game.
"We have got lots of big games coming up in the next few weeks and the idea is not to rotate the squad, but to give some players a bit of rest, and it was Berbatov's turn."
There was also praise for Jamie O'Hara, who was introduced for Kevin-Prince Boateng at half-time. "I think it was a bit 'hurry-scurry' in the first half," added Juande.
"We needed someone like Jamie to put his foot on the ball, slow the game down and get hold of the ball and pass it a little bit more.
"I think that brought a little bit more order to the game and he did that very well."
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Juande Ramos felt we gradually wore down Derby as we ran out 3-0 winners at Pride Park on Saturday.