Rosberg kept his cool amid the chaos to win the crash-marred race on Sunday to give Mercedes its first victory of the season, as well as matching Keke Rosberg's Monaco victory from 1983 — the year after Rosberg Sr. won his only F1 title.
But Rosberg is only sixth in the overall standings and is still 60 points behind leader Sebastian Vettel.
"I don't want to talk about (the title) at all," Rosberg said. "We should not get over-excited for the next couple of races. We still have a bit of an issue with our race pace, and also with the development race, everyone is pushing forward. So I am definitely not thinking of the championship, I am today just thinking about Monaco."
He played down the emotional significance of matching his father's achievement.
"It's special, but honestly that's not what I was thinking of when I was crossing the finish line," Rosberg said.
Still, he did enjoy the occasion of winning only his second career GP in the place where he spent much of his childhood growing up.
"This is the most special race for me to win, it was incredible, unreal. That is what is special about the sport," Rosberg said. "When I was quite young watching this race, my first memory was Ayrton Senna with the yellow helmet in the red and white (car)."
Rosberg began from pole position for the third straight GP, but he had to re-start three times after the race was held up by a safety car, a red flag and the safety car again.
The German finished ahead of Vettel and his Red Bull teammate Mark Webber. Lewis Hamilton finished fourth after starting from second.
The red flag came out with about 30 laps to go when Williams driver Pastor Maldonado was nudged into the wall by Marussia's Max Chilton.
Earlier, Ferrari's Felipe Massa crashed and the safety car came out a second time when Frenchman Romain Grosjean smashed his Lotus into Daniel Ricciardo's Toro Rosso. Grosjean was handed a 10-grid penalty point for the Canadian GP in two weeks' time.
After winning, the 27-year-old Rosberg danced on the bonnet of his car before jumping off to hug team members.
Rosberg won his other race from pole at the China GP last year and his previous best result this season was fourth in Malaysia.
They were useful points for three-time defending champion Vettel, who extended his lead at the top of the standings to 21 points over Kimi Raikkonen and 29 over Fernando Alonso, who failed to repeat his Spanish GP win from two weeks ago and could only manage seventh place.
Raikkonen finished way down in 10th after being barged by McLaren's Sergio Perez late on.
"I'm very happy and pleased with the result," said Vettel, who started from third on the grid.
Crashes dominated as Monaco confirmed it is one of the most difficult tracks in F1.
Chilton lost control and moved across into Maldonado on his side, sending the Venezuelan off the wall and into the crash barriers. Chilton's teammate Jules Bianchi was dragged into the crash but no driver was hurt.
Massa, meanwhile, ploughed into the wall and slid across the track in a carbon-copy of his crash in Saturday's third practice. He was released from hospital after check-ups.
It was eventful off the track, too.
A little more than one hour before the race, Red Bull launched an official protest against Mercedes.
Red Bull team principal Christian Horner demanded clarity as to why Mercedes was allowed to conduct in-season tire testing following the Spanish GP.
Rosberg refused to answer questions about the issue in the post-race press conference.
Early on, Frenchman Charles Pic's race ended when he had to bank his Caterham onto the side of the track and quickly clamber out as flames started shooting up. He was unhurt.
Hamilton had just pitted for new tires on Lap 30 when Massa crashed. As a result, when the safety car first came out, it was cruel on Hamilton, who then dropped behind Vettel and Webber — last year's winner — and into fourth place when the race re-started.
"I don't put it down to bad luck," said Hamilton, who is fourth overall and 45 points behind Vettel. "I wasn't good enough."
Mini-battles raged everywhere before the red flag came out on Lap 46, and the race was halted for the third time on lap 62 after Grosjean lost control coming out of the tunnel.
There was still time for another incident when Perez tried for the second time to get past Raikkonen on the inside and then failed to finish. They both blamed each other.