However, his team also warned the 20-year-old, who crashed again in practice, to keep his overtaking clean for the rest of the race.
It was his first Monaco victory, his second this season and the seventh of his career, but a landmark feat heralded by his team boss Christian Horner. Between the transmission and engine faults, broadcasters reported Ricciardo as being down as much as 30 kilometers per hour (18 miles per hour) on the straights-a crippling weakness even at Monaco, which put him as much as 10 seconds per lap down on his record-setting 1:10.810 pole time.
"I know what I have to do and what not", said Verstappen.
"Two years in the making and I finally feel redemption has arrived", Ricciardo said. I felt a loss of power and I thought the race was done.
The Brit, 33, later said: 'We were just cruising around from lap six, literally cruising, so it wasn't really racing.
Ferrari's Sebastian Vettel and the Mercedes of Lewis Hamilton completed the podium but the pair didn't have the tyre life or the space on the tight city street circuit to make any serious move on the ailing Ricciardo.
On team radio earlier, the Briton said: "Thank God that's over". Others - including some of the sport's biggest names - argue that it was the most boring race in F1 history. "They had the pace all weekend, as we knew they would". Maybe we need two races?'
Having missed qualifying because his vehicle could not be repaired in time following his FP3 shunt, Verstappen then had to watch on as team mate Daniel Ricciardo captured pole. Then he was a bit stronger there and we couldn't follow.
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Two-time champion and former Monaco victor Fernando Alonso was seventh for McLaren ahead of Carlos Sainz of Renault, Sergio Perez in the second Force India and Pierre Gasly of Toro Rosso.
The Australian led from pole but a powertrain issue midway in the race kept everyone on their toes, while bringing back memories of 2016's race where a pit stop error cost him the win.
Lewis Hamilton kicked off the pit war with a stop after lap 12, emerging behind Esteban Ocon who allowed the Brit back past on lap 15 as Vettel dropped in for tires. Pirelli had been asked to provide new softer tyres to give the chance for quicker lap times.
Ricciardo was told by his race engineer the problem would not improve, with the Australian left to try to cope with his vehicle with still over half of the race left to go. "I just wanted to see my name on top and keep that momentum going".
A couple of weekends ago, I spent a good chunk of time watching on, feeling rather envious of my friends and colleagues out at the Monaco Grand Prix Historique.
By lap 32, Ricciardo's lead was down to 1.2 seconds with Hamilton nine seconds adrift in third.
"Obviously in the top areas there's only Ferrari and Mercedes he could ever consider, but now here that's unlikely, I don't think that's going to happen", Hamilton said.