Portsmouth 2-1 Crystal Palace
Scott Allan and Greg Halford were on target as Portsmouth kept their slim survival hopes alive.
Allan opened the scoring with a deflected effort in the first half and Halford added a second with a header.
Darren Ambrose pulled one back for the Eagles with a penalty but even though Pompey held on for the victory, their prospects are slim.
Michael Appleton's team are five points from safety with just two games left and could be relegated at the weekend.
But Bristol City's 1-1 draw with West Ham ensured there is still a chance for them to avoid dropping into the third tier for the first time since 1983.
Palace had made the better start but the hosts pulled in front just after the half-hour mark.
Luke Varney's effort came back off the post and Allan's shot hit Nathaniel Clyne to leave Julian Speroni stranded for Scottish midfielder Allan to record his first goal in English football.
Ten minutes after the break, his cross was met by a powerful header from Halford.
Midway through the second period, Varney clipped Wilfried Zaha in the area and Ambrose thumped in from the penalty spot.
Ambrose also missed with two late efforts from long distance that could have sent the hosts down.
Portsmouth boss Michael Appleton: "All the pressure is on Bristol City as far as we're concerned.
"There's no pressure on us. It's for them to throw away rather than us to achieve it.
"We knew if we'd won the game and they'd beaten West Ham, we would have been down anyway. We can't control their results. We can just control our results.
"We'll try and win again on Saturday and we'll give it everything we have got because we've got pride and we've got dignity. If the worst-case scenario does happen, hopefully we can do it with a little bit about us."
Crystal Palace boss Dougie Freedman: "We didn't take our chances. I thought our performance was fantastic pretty much from start to finish. I cannot criticise the players' work rate.
"It was a night where we played some fantastic football; our attacking display was great. We just couldn't quite get the goals I thought we deserved. It was a difficult result to take after looking at our performance."