Well had missed five good chances, most of them falling to lively teenager Craig Moore, before Sutton was allowed time and space to convert a diving header on a counter-attack.
Anier came off the bench to create a late second for himself as Motherwell moved into third in the Scottish Premiership following a run of three defeats in four games.
McCall, who had asked full-backs Fraser Kerr and Zaine Francis-Angol to overlap, said: "We set up to play in a slightly different way and after taking a little while to settle we got into a good pattern. The full-backs got high and wide and got some really good balls in.
"We were disappointed to come in at half-time and not be ahead. But we had a clean sheet and a really strong, positive performance.
"Sometimes when you miss chances it comes back to haunt you. Thankfully that wasn't the case and Henri's goal put the icing on the cake.
"The last four games, even though we beat Hibs, we have not performed at a great level. Today we were back more like ourselves. We were strong and resolute when we needed to be and also played some good football."
McCall brought off James McFadden for Lionel Ainsworth at half-time and praised the former Everton player for his reaction.
"He is trying like an absolute bear," McCall said. "He is so wanting to do well that he is trying that hard at times. But when I brought him off at half-time he was terrific in the dressing room, encouraging everyone else.
"Things will come good for him if he keeps putting the application in, which he is doing. But then Lionel gave us a bit of pace and is a little more direct."
Kilmarnock manager Allan Johnston was again left to bemoan some slack defending.
Johnston, whose side should have levelled midway through the half when Kris Boyd missed a free header, said: "When you look at the performance, I don't think it merited a 2-0 defeat. But how many times can we keep saying the same thing?
"We created a few good chances but teams don't need to work hard to score against us and that's been a problem since we came in.
"Sutton caused us problems with his strength and we just couldn't cope with it at the back, whereas at the opposite end their centre-halves made it a lot more difficult.
"There was loads of mistakes for the first goal. It came from our corner. They have got one striker up the park and we have two back and he manages to hold the ball in.
"Then the ball gets played across the face of goal, comes out the other side and comes back in again and Sutton is still standing himself, and we have three or four players round about him. It's just basic defending, you pick someone up.
"And the second goal we just got bullied. It's very poor defending."
- Sports & Recreation
- Scottish Premiership
- Craig Moore