Quick-fire goals from Darius Charles and John Mousinho added to Jimmy Smith's first-half strike as the home side stretched their unbeaten run to four league games.
Curtis Obeng's own goal with two minutes left was nothing more than a consolation for Rovers.
Despite the victory - a third in the last four games - Boro remain in the relegation places but Westley believes that could all soon change.
"We were strong, it was a determined display, we did what we had to do and it was quite convincing on the whole," said Westley, whose team are now just a point from safety.
"I wanted us to play on the front foot and take the game to them and I thought the change worked well. We put them under more pressure and showed more positivity in the way we played.
"Like I keep saying, we knew to be a League One club we need to win a certain number of games. To get into the top half, which is our objective, we've got to win a lot of games.
"We're three wins out of four now which is a good bounce back from the situation we've been in.
"We're not complacent, we know the top sides have nicked results against us and we're hoping that we've made enough improvement in the last two or three games to match another top side on at Preston on Tuesday and this time do better than we've done previously."