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."
Martin Jol described the victory against Manchester City as a 'crucial moment in the season'.