City recovered from an early injury to in-form striker Gabriel Jesus, with Raheem Sterling's opener before the half hour and a Tyrone Mings own goal in the second period securing the points.
Guardiola's men kept only their sixth clean sheet in 25 top-flight matches as they moved up to second, eight points behind leaders Chelsea, and he was delighted by how Silva orchestrated closing out the contest on the front foot.
The core of the side who won City's first Premier League title in 2011-12 have endured a chequered existence under the former Barcelona coach.
Joe Hart was forced into a season-long loan with Torino when it became clear he did not feature in Guardiola's plans, Yaya Toure endured a spell out in the cold, and Sergio Aguero and Vincent Kompany again started on the bench at Bournemouth.
"He was amazing," Guardiola said during a post-match news conference. "In the last 15 or 20 minutes he monopolised the ball with Kevin [De Bruyne], with Fernandinho, with all the players.
"We passed and passed and passed — it is the best way to avoid the opponents. You have the ball; there is just one ball. We have just to control the counter-attacks and it's safer.
"We did it, for the first time this year. For the last 15 to 20 minutes we controlled the game.
"My feeling and impression after the Tottenham game [a 2-2 draw at the Etihad Stadium last month], when we played amazing and were unlucky not to win, is our game is more stable.
"Everybody knows what they have to do and that is why we have more confidence."
If Silva provided the stability, it was Leroy Sane's livewire wing play that brought box-office thrills to City's third straight league win.
Full-back Adam Smith endured a particularly torrid evening at the hands of the Germany youngster and, after watching Sane make a tentative start to life in the Premier League as his form and fitness failed him, Guardiola feels the close-season arrival from Schalke is like a new signing.
"The people say in the winter transfer window one guy arrived with Gabriel Jesus. I think we had two arrive," he said, before pointing towards the significance of Sane's maiden City goal in the 2-1 December win over Arsenal.
"Leroy came here a little bit scared but I think after the game against Arsenal something clicked.
"He has showed us a lot of things. He is so fast, his intensity helped us a lot and he helped us defensively too.
"He is only 21 years old. I am so happy for Manchester City. We have a good player for the next years."