The hosts stalled Rotherham's promotion charge as goals from Peter Winn, Byron Harrison and Scott Laird secured all three points for Boro in a comfortable victory.
Westley said: "This is a terrific result for us, and we deserved it. The lads were exceptional throughout and this result gets our league campaign right back on track.
"We played some particularly good football against a Rotherham side who have been right up there pretty much all season.
"For whatever reason they've suffered a little blip now, but it's all about us and what we do and this will give everyone a lift going into the cup game at the weekend.
"I was pleased we got the two goals late in the game as up until then there was always that chance Rotherham might catch us out and grab a point. We've scored some quality goals too."