Robbie Keane's late winner took us to within two points of fifth-placed Liverpool on the final whistle although the table soon changed with Bolton beating Norwich City in the evening kick-off.
Nevertheless, we remain in ninth spot, just four points behind Bolton in fifth and two adrift of Liverpool in sixth.
Like Charlton on Wednesday night, it was another scrappy encounter with Jermain Defoe heading us into the lead after 16 minutes only for Claudio Reyna to level just before the break.
It looked like ending a point each before Keano turned home Simon Davies' deflected shot with six minutes left.
Head Coach Martin reflected: "Everybody would have told us that had we not won that the rest of the season would be bleak, grey.
"This was our third match in six days and came after three away games where I think we've been the better team and not won.
"I was resigned to a draw because they kept on breaking on the counter-attack and it was difficult. We had to make a choice playing at home to play with two strikers high up but they had Bosvelt in midfield, so we had to find a way around it.
"All we could do was battle. Sometimes you play well and don't get the points but this was the reverse. I was really happy with them and I'm sure the supporters will be pleased as well and forgive us for not having the best game of the season because we've played well at home."
Stuart Pearce felt his City side deserved some reward from his first game in charge at the Lane on Saturday.
Caretaker boss Pearce sent out a side tough to break down in a 4-5-1 system and they looked set for a point after Claudio Reyna cancelled out Jermain Defoe's opener in the first half.
But enter Robbie Keane, the substitute was on the spot six minutes from time to tap home the winner.
"A draw was probably a fair result," said Pearce. "Maybe we ran out of legs in the last 15 minutes which cost us a touch. I think we had as many decent chances as them during the game.
"There was a lot of encouraging things for me. I was pleased with the spirit we showed. I have been for the last week."
Pearce knows he needs results between now and the end of the season or his caretaker role will not be made permanent.
He added: "The result was very disappointing because I am in a results business. Being stuck on the touchline and being reasonably fit still, I was tempted to jog up that line once or twice. But you have to counter that feeling and hope that the players you send out have the same spirit.
"I was very proud of them and had we been a bit cuter in front of goal we might have snatched the game. The lads have done extremely well in my eyes but we haven't got a result. But if we keep on doing that, we will end up winning more than we lose."
Martin Jol described the victory against Manchester City as a 'crucial moment in the season'.