Goals from Wilfried Zaha and Christian Benteke helped Palace to victory after Cesc Fabregas had opened the scoring early on and Allardyce was all smiles after his side moved on to 31 points from 29 games.
"I think our performance was typical of this side's character. We went behind so early, but the character of this team shone through with a quick response," the Palace boss said.
"Our defending was outstanding, as was our goalkeeper. We could have scored even more. The gameplan worked exceptionally well. We played a slightly different 4-4-2 with our two attackers out wide.
"These are three very sweet points against the team that will be champions. This is what the Premier League is all about. We have made the people notice us. It is an outstanding performance for everybody at Palace.
"We are on to 31 points now. Our main aim remains to be safe. But injuries are a reason for concern, with a game coming up on Wednesday [against Southampton]. But the guys who came on did really well. We hope for more points on Wednesday and then want to push on.
"It is ours to throw away. When you have more points than games played at the end of the season, you are safe. We are in that position now."
Mamadou Sakho was equally pleased with Palace's display and believes they have a good chance of staying up after making it four league wins in a row.
"We played a good game. It was really hard but I think we played with a big heart," Sakho said.
"Our fans really shouted for us and they gave us a lot of encouragement. We played 12 against 11.
"It was important to come and win here. We spoke at half-time about needing the three points. We were not here to go back with a draw.
"We played with big determination. I am so happy for us. It is a good team with good players and we are starting to believe. If you fight like it is your last day, you can reverse everything."