Vettel closed to within one second of Ricciardo with more than half of the 78-lap race left.
"Absolutely wonderful, I don't know how you did that, Daniel", said engineer Simon Rennie.
Ricciardo is the key cog in this year's driver market and has raised his value with two highly-praised wins in China and Monte Carlo.
Hamilton now sits on 110 points in the 2018 Drivers' Championship.
"We knew we wouldn't be the quickest here, just did the best we could", Hamilton said. Couple this with the difficulty required to make a pass in Monaco and you get exactly the kind of race we had on Sunday. "And it feels good".
Hamilton, a four-time world champion and the current leader in the drivers' standings, was equally scathing, saying "it wasn't really racing". "Thanks to the team". "I thought the race was over".
As he did immediately after the race, Hamilton joked that he had offered his managerial services to Ricciardo - his first bit of advice was to look at the potential of his current team.
Red Bull reckon they will be on the pace in Montreal in two weeks too, so hopefully normal F1 service will be resumed in a six-way fight with great supporting acts. "We knew that would be the case".
For the first time since 2009 the race had no need for a safety vehicle, which leads the cars around at reduced speed while debris or other obstructions are removed.
Vettel said it had been a tricky race and "Daniel had the answer at all times".
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Daniel Ricciardo may have started from pole position in Monaco, but despite this advantage on the overtake-resistant street circuit, his race would prove anything but easy.
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.
Hamilton stopped as early as lap 12 and had to manage a set of ultrasofts for the remaining 66 laps.
Everything went pear shaped when Ricciardo radioed in to tell his team that his auto was losing power.
"If at some stage Red Bull get an engine [closer in performance to Mercedes and Ferrari], they are going to be even closer to us".
'We probably need to give something to the fans at the end of the race just to pay back the ticket'.
"Will it get better", a desperate Ricciardo asked over the team radio. Could Hamilton and Sebastian Vettel survive without pitting for a second time?
"So much went on for me in that race, trying to figure out what was going on", said Ricciardo, who was fastest in all three practice sessions as well as qualifying.
"It's almost impossible to overtake, but it's still one of the most fascinating races", Vettel said.
By lap 50, they were separated by only 2.6 seconds.