Rosberg controlled the race from the front and victory gives him fresh hope in the Formula One championship battle -- cutting Hamilton's lead to just two points.
Hamilton was looking to extend his lead over Rosberg at the Italian Grand Prix after qualifying nearly half a second quicker than his fellow Mercedes driver but he quickly dropped down the order after failing to get away cleanly.
Hamilton fought his way back up the order but couldn't catch the flying German.
Sebastia Vettel joined them on the podium and his Ferrari team mate Kim Raikkonen was fourth, bringing joy to the Italian team's fans.
'Great day for Mercedes'
After the race, Hamilton told the crowd: The start wasn't great but it was still a great day for Mercedes and I'm proud to be part of it."
Rosberg was in upbeat mood after scoring maximum points, telling reporters: "It was all down to the start. I had an awesome start and that made the win. I am feeling great. The race is on with Lewis. It is always going to be a great battle and I look forward to what is to come."
Hamilton added: "Look at this crowd. This is the best crowd we get all year. This is incredible."
By starting at the top of the field Sunday, Hamilton equaled the record of Ayrton Senna and Juan Manuel Fangio in claiming a fifth career pole at the legendary Monza track.
But the disastrous start prevented him becoming the first driver since Fangio in the 1950s to claim a hat-trick of consecutive victories at the circuit.
Rosberg takes advantage
The momentum has swung back in Rosberg's favor with back-to-back wins and after it looked like Hamilton was starting to pull away in his bid to win his fourth world championship.
The F1 website points out that the Mercedes team's one-stop strategy
-- starting on soft tires and finishing on mediums -- also helped secure victory over the Ferrari duo who elected to stop twice.
Mercedes has a comfortable lead in the constructors' contest but Ferrari has closed the gap on Red Bull.
Earlier Saturday it was announced that former F1 champion Jenson Button will not be on the F1 grid in 2017. And Williams driver, Felipe Massa, said earlier this week that he would be retiring at the end of the 2016 season.