The Black Cats had a first-half lead through Eliezer Mayenda before Evanilson struck an equaliser just over the hour mark.
Ballard said afterwards: "It was an intense game. It's a tough place to come here. They bring high energy. All the duels are tough. We've struggled of late and we needed to bring it back to basics. We did that and we matched them."
On captain Granit Xhaka returning, he continued: "We've missed him of late and we've had our toughest run of the season. To have a natural leader like that come into the team is great. It was important to bounce back. I think we've done that today.
"They put you under pressure all game. It's hard to have control of the ball, it can feel end to end. It's a tough place to come so we can be proud of the performance today."
On Sunderland's first-half penalty shout, Ballard added: "It felt like it was a penalty at the time. I've not seen it. It's a tough job to referee, especially on a day like today where both teams are going on it. It's difficult for them, but it did feel like a penalty."