Xhaka smashed home a free-kick as Arsenal beat the Blues 3-1 on Boxing Day to secure their first Premier League win since November 1.
The goal was a timely one for Xhaka, who was making his first appearance since returning from a three-game ban.
The midfielder was sent off during the defeat to Burnley earlier this month after grabbing Ashley Westwood by the throat.
Not for the first time in his career, Xhaka came under fire for his behaviour but he responded by excelling against Chelsea.
“There was a lot of speaking after the red card,” he said. “A lot of people started speaking again… and again and again. I will always show my character.
“I was very disappointed about my red card and I knew what I did was wrong for my side. But I am more than happy. I helped the team today and I am back.
“We got the three points back after dropping some in the past few weeks.
“We knew it would be a very difficult game, but I think we worked very well together today like a team and at the moment we can only get points if we do this.”
Arsenal’s win over Burnley eased the pressure on manager Mikel Arteta and moved them away from the relegation places.
The Gunners are now six points clear of the drop and can move further away in the next week as they take on Brighton and then West Brom.
“It was very important that we got three points today, but we have to continue like this,” Xhaka added.
“The next two games away are very difficult, but if we work together like a team as we did today we have the chance to take away all six points from the next two games.”