If Sunderland take at least a point at home to Stoke tonight and Wigan beat Swansea on Tuesday, Newcastle could be in the bottom three for the first time all campaign.
And Gutierrez, still haunted by that relegation four years ago, can barely believe it.
After their draw at West Ham United, Gutierrez, 29, said: "I think we showed that was a performance of a united, committed team. Everybody could see we were fighting for each other.
"It has been a difficult few weeks and we haven't been solid or compact but today we were. We walked off the pitch and heard the other results but really I don't care about the other teams, I'm only thinking about Newcastle and what we have to do.
"This result was a good step in staying up. Away from home we haven't had many good performances this year, now we look forward to the next game and hopefully the same kind of performance can get us a win.
"No one who was here could say we weren't playing for each other, fighting until the final whistle. If we'd played more games like this in recent weeks I don't think we'd be talking about a relegation battle.
"We showed the fighting qualities we need to survive."