As City eased towards a 25th Premier League match unbeaten, Silva could have had a hat trick, missing an easy chance before linking superbly with Raheem Sterling in the 52nd minute, and Aguero finished the rout five minutes from fulltime.
City are 11 points clear at the top of the table and are really looking the absolute business. For me, one of the best sides I have ever come across.
But it was City's history boys who grabbed the headlines, and Guardiola added: "Records are there to be broken but at this level it is so competitive - the managers, the players, the analysts - and that means we are strong in the head".
The Hammers nearly completed a smash-and-grab in the end but substitute Javier Hernandez's shot from Mark Noble's pass hit the bar and bounced off the line.
Liverpool also wasted an opportunity to stay in touch with the clubs at the top of the table as they were held to a frustrating goalless draw by West Brom.
"We have had games when we've looked toothless and not going to score, but we did get up in their end a few times", Clement said about his side, "but they were desperate to keep a clean sheet, throwing bodies in front of the ball, it's the mark of a great side".
Silva has now scored four goals in his last three games and was at his brilliant best here, conducting the City orchestra with his passing and movement.
In the second-half Liverpool saw young striker Dominic Solanke have a goal ruled out and were given a scare as Hal Robson-Kanu struck the crossbar with a long-range effort. The former PSG man opened his account for the club in freaky fashion, his cross evading everyone in the box and going in.
Sam Allardyce continued his undefeated start as Everton manager with Wayne Rooney's tap-in enough to beat Newcastle, who sit a point above the relegation zone.
While Clement was disappointed to lose the game, he conceded that fixtures against the likes of Manchester City are not where he is targeting points.
Speaking after the game, Guardiola said: "Considering we have a lot of games in our legs, a demanding game at Old Trafford three days ago, we were solid, we were serious and we made a good performance".