After a scrappy start in the third round replay, Aaron Lennon's opener on 26 minutes paved the way for a 3-0 interval lead with Robbie Keane and Steed Malbranque also on target.
The second half was a quieter affair as Jermain Defoe wrapped it up with the fourth goal in the 80th minute.
Martin said: "We were a bit worried after the last two home games (defeats to Liverpool and Newcastle) and we knew we had to win this one.
"We wanted to stay in the FA Cup because it is important for us.
"Cardiff gave us a tough game away from home so we knew we had to start at a high tempo, try to be creative and score some goals.
"We didn't do it at the start but then we scored the goals and that was a good spell. We played well in the first half and picked up where we left off against Newcastle, playing good football.
"I didn't want to make too many changes although it will be difficult not to with so many games coming up but I feel the FA Cup deserves us to play with almost our best team."
We will now take on Southend United at home in the fourth round on Saturday January 27, kick-off 3pm.
Martin Jol was pleased to get back to winning ways at the Lane and book a place in the fourth round of the FA Cup with Wednesday night's 4-0 win against Cardiff.