Leon Constantine struck just after the hour to hand the visitors the lead and convince Martin to throw Dimitar Berbatov into the action from the bench. Aaron Lennon had entered the fray seconds before Constantine's goal.
Vale keeper Mark Goodlad was in inspired form throughout and saved everything we could throw at him until the 79th minute, when Tom Huddlestone's perfectly flighted inswinging free-kick just evaded Dorian Dervite's head and went in off the post.
That took the game into extra time and Goodlad produced the pick of an impressive bunch of saves just a minute into the first period, somehow reacting in time to tip over Dimitar Berbatov's flick.
However, it wasn't long before Huddlestone connected with a screamer from 30 yards to put us 2-1 up and Jermain Defoe ended it as a contest in the second half of extra time, converting Phil Ifil's cross to finally beat Goodlad.
"Everybody expects you to go through to the next round, it's the same as it always is," said Martin, who handed debuts to fit-again Steed Malbranque and youngsters Andy Barcham and Dervite. "But Fulham, Man City, West Ham and Man United all went out.
"All the ingredients were there for an upset - they were organised with an outstanding goalkeeper, they gave us the initiative and that is not easy.
"We had five chances in the first half but it was one of those games where the ball wasn't going in the net.
"But I felt home advantage was there, we kept believing in the second half and we had some outstanding performances.
"I was concerned but luckily our quality probably gave us the edge, Dimitar Berbatov gave us that little extra and Aaron Lennon showed a good mentality when he came on.
"We had 34,000 fans in the stadium and the lads knew that, Edgar Davids was skipper and said before the game how important it was to go into the quarter-finals. We showed good character in the second half to grind out the result."
Martin Jol admitted he was concerned as we trailed 1-0 with time ticking away in Wednesday night's Carling Cup clash against Port Vale but felt that our extra quality saw us into the quarter-finals.