Silva was City's first signing last summer, joining at the end of May for £43 million (S$78.6 million) from Monaco, where he had enjoyed a run to the semi-finals of the Champions League.
It was Aguero's 14th goal in 11 games in 2018.
"It's an fantastic result.We were clinical today and that's so important in this competition".
"It's the Champions League and it's always tough - we didn't concede which was the most important thing after these goals".
Gundogan scored again after half-time to put City in a commanding position ahead of the return leg at the Etihad on March 7.
Four minutes later, Pep Guardiola's side doubled their advantage on the night as Bernardo Silva found the top corner from inside the Basel box, although the home side's goalkeeper might well feel that he should have done better.
"We are nearly there in the quarter-finals".
If we are able to go to the quarterfinals, that's better than last season.More news: United States urges help for Iraq, extends $3 billion credit line
Although City handed out a crushing 4-0 defeat to FC Basel they still have a long way to go before getting their hands on the Champions League trophy.
Vincent Kompany believes that such spirit and form is just what the club needs to lift the Champions League title apart from the experience they have gained in their six stints in the competition.
Four minutes later, Leo Lacroix failed to cut out Raheem Sterling's cross and the unmarked Silva lobbed his shot over Tomas Vaclik's attempted save, then Aguero scored the third from outside the area - City's fourth shot on target of the game.
"The Champions League is 180 minutes, but we are nearly there", said the Spaniard.
City's double goalscorer Gundogan said: "The result was maybe flawless but the way we played there are still plenty of things to improve". Kevin De Bruyne also recorded his 19th assist of the season.
"If we play like we did today and in the past few weeks", Gundogan said, "we will be successful, for sure".
"In these kinds of situations, in my opinion, if we have this game at the Etihad and it's a 3-2 or a 2-2 draw, that won't give us a good feeling going into the next round", he said.
Having gotten favourable results in their first leg ties, Man City and Spurs will hope to seal their passage to the quarterfinals in a fortnight.