Ricciardo held off Sebastian Vettel for Ferrari and title leader Lewis Hamilton in his Mercedes despite suffering a loss of power just before halfway in the 78-lap race on the testing street circuit.
It was his seventh career win and just reward after his 2016 disappointment in Monaco when a late pit stop error cost him certain victory and left him devastated.
"It was two years in the making this and I really feel that redemption has arrived," Ricciardo said after taking the checkered flag.
"After the loss of power I thought the race was done, but I got home using just six gears," he added.
Vettel, like the other frontrunners was struggling with tire wear, but has closed the gap in the standings to Hamilton to just 14 points after six rounds of the championship, with Ricciardo 24 points further adrift in third.
Kimi Raikkonen finished fourth in the second Ferrari, with Hamilton's teammate Valtteri Bottas in fifth.
Ricciardo's Red Bull teammate Max Verstappen carved his way through to ninth having started at the back of the grid after being unable to take part in Saturday's qualifying following an earlier crash in practice.
While it was a case of what might have been for the young Dutchman, Ricciardo was left to celebrate a hard-fought victory which looked to be slipping from his grasp when he reported losing power and his pace immediately slowed.
"Just keep focused" came the reply back on team radio, aware that overtaking is notoriously difficult on the Monaco circuit.
Ricciardo did just that, having dominated all the practice sessions before claiming the second pole position of his career Saturday.
A clean start left him clear of Vettel, who was only able to seriously challenge after Ricciardo's technical issues, but was still unable to force home his advantage.
"I think we had the pace, but it was a tricky race," admitted Vettel. "I started to pick up a bit but then lost a bit in my tires."
Hamilton, who had won the previous two rounds, also briefly scented victory as the field closed up, but also slipped back by the end.
"First of all, congratulations to Daniel and Red Bull, they did a great job.
"I did everything I could. It was the least interesting race," said the Briton.
Ricciardo's victory was a fitting way for Red Bull to celebrate its 250th race in Formula One, during which time it has secured 57 victories and 113 podium finishes, not to mention taking pole on 59 occasions.
Attention now turns to the Canadian Grand Prix in Montreal in two weeks time, with three drivers, Ricciardo, Vettel and Hamilton on two wins apiece this season and dueling it out for the world title.
Both Hamilton and Vettel are seeking a fifth world championship crown with Ricciardo hoping for his first in an improving team.