"Lewis did a great job and deserved the win.
"I gave it everything, but not enough. I tried everything but Lewis knew how to react."
Rosberg was in a rush to leave the circuit since his wife is expecting their first child "any time."
Mercedes driver Lewis Hamilton leading at the first corner during the Belgium Formula One Grand Prix at the Spa-Francorchamps circuit last night. Picture/AP.
The two Mercedes cars were dominant throughout the race, unlike the previous Grand Prix in Hungary three weeks ago when they failed to make the podium.
"Nico had good pace but I was able to answer all the time. At the end when I saw a tire had blown on another car, I was very cautious," Hamilton said. "I was fairly relaxed at the end, the car was fantastic all weekend."
Hamilton's 39th career victory " and second in Spa " gave him a 28-point lead over Rosberg in the drivers' standings, with eight races remaining. Hamilton is seeking his third championship.
Romain Grosjean of Lotus was third, taking advantage of a late puncture for Ferrari's Sebastian Vettel, who ended outside the points in 12th place.
On Lap 32, Ferrari told Vettel over team radio that the tires looked "pretty good to go to the end. " But in the 42nd and penultimate lap, his rear right blew out as Grosjean kept up the pressure on the Ferrari driver.
"It was a bit scary being behind," Grosjean said.
Vettel was on a one-stop strategy and the risk did not pay off, leaving Ferrari without a podium finish in its 900th Grand Prix. The German driver is now 67 points behind Hamilton in the drivers' standings in third place.
Grosjean made his first podium since finishing second in the U.S. Grand Prix in Austin, Texas, in 2013. He was banned for one race after being blamed for causing a multi-car crash at the start of the Belgian Grand Prix in 2012.
"I can't believe I am on the podium," Grosjean said.
Grosjean started from ninth position on the grid after being penalized five places for an illegal gearbox change.
Lotus has been involved in problems off the track, with Belgian police threatening to impound the cars because of money owed to a former reserve driver.
"Of course at Spa I still remember Turn 1 in 2012, but I think that made me stronger," Grosjean said.
Hamilton's winning time was one hour, 23 minutes, 40.387 seconds for the 43 laps on the 7-kilometer (4.35-mile) circuit, the longest and among the fastest on the Formula One calendar. The race was cut by a lap because the first start had to be abandoned when Nico Hulkenberg's Force India lost power.
Daniil Kvyat was fourth in a Red Bull, Sergio Perez finished fifth in his Force India after climbing as high as second during the race, Felippe Massa was sixth in a Williams and four-time Belgian GP winner Kimi Raikkonen seventh in Ferrari. Also in the points were Max Verstappen in a Toro Rosso, Valtteri Bottas in a Williams and Marcus Ericsson in a Sauber.
Bottas started third but also messed up his start and then had a drive-thru penalty when his team put the wrong tire on one of the wheels.
Red Bull's Daniel Ricciardo, last year's winner in Spa who was battling for a podium finish, had to drop out in Lap 21 when his car lost power.
Lewis Hamilton (GBR) Mercedes 227
Nico Rosberg (GER) Mercedes 199
Sebastian Vettel (GER) Ferrari 160
Kimi Raikkonen (FIN) Ferrari 82
Felipe Massa (BRA) Williams 82
Valtteri Bottas (FIN) Williams 79
Daniil Kvyat (RUS) Red Bull 57
Daniel Ricciardo (AUS) Red Bull 51
Red Bull 108
Force India 49
Toro Rosso 35