Palace manager Roy Hodgson felt his side had been building towards this result after improving displays on the road in recent weeks.
Goals from Christian Benteke, Wilfred Zaha and Bakary Sako delivered a first away of the season for Palace against Leicester, with Benteke getting his first goal since May to open his side's account on 19 minutes.
He followed that up with an assist for Zaha's fourth goal of the season five minutes before the break.
Speaking after the game, Hodgson said he was pleased with the victory, but stressed that his players have been gradually working towards a winning performance away from home.
"We've been getting closer and closer and today it all fell for us. I'm delighted with the victory, but I'm not that surprised because we've been threatening to do that for quite a long time now."
Hodgson was particularly happy with Benteke's influential performance being recognised by the travelling fans.
The former England manager added: "I think the crowd appreciate not just the goal, but the fact that Christian was working so hard in the other aspects of his game as well.
"They were singing his name which was fantastic because after missing the penalty he perhaps rightly, many people were saying, got some stick from the crowd.
"But on this occasion they've turned very quickly singing his name and that was fully deserved."
Meanwhile, Leicester boss Claude Puel was disappointed with his side's performance as they finished the last half hour of the game with 10 men.
Birthday boy Wilfred Ndidi was dismissed with two yellow cards, the second of which was distributed for diving in the Palace penalty area.
"It was not a good day for us," admitted Puel after the game.
"I think our play was too slow against a good team. We needed to have more quickness, more quality on the play and it was not possible today.
"It was not our day, it was not a good game for us. Crystal Palace deserved this result; they played with desire, togetherness and quality. We didn't deserve a win today."
