Ricciardo took the lead with just 10 laps to go when he charged past then-leader Valtteri Bottas, who ended up second in his Mercedes.
After the Chinese Grand Prix, Vettel still tops the drivers ranking ahead of Ferrari duo of Hamilton and Bottas, while Ricciardo moves into fourth following his victory.
Bottas admitted feeling a bit hard done by in his 100th grand prix, particularly since the timing of the safety car's deployment didn't allow him to stop for tyres when the Red Bulls did. The soft tires paid in the end, as both Ricciardo and Verstappen had incredible pace in the final minutes.
"We were going pretty well and we were looking strong until the safety auto", he said.
"Holy Testicle Tuesday", the 28-year-old exclaimed if asked exactly what his reaction could have been had someone suggested that Red Bull would acquire a race earlier winners Mercedes this season.
Mercedes' Hamilton missed out on the podium for the first time this season, crossing the line fifth behind Verstappen.
"Sometimes you've just got to lick the stamp and send it", he said in classic Ricciardo fashion.
There will be a post-mortem at Ferrari as to how they let that happen, given Vettel was leading by more than three seconds before Bottas' stop on lap 19 on 56, with Vettel stopping a lap later.
Frustrating results for the Scuderia Toro Rosso driver Pierre Gasly who took 18th position and Bredan Hartley who DNF after the teammates had a mild collision. The "honey badger", as he refers to himself, was relentless in his pursuit of race leader Bottas and on lap 46 he dived down the inside of the number 77 Mercedes at a right-hand turn and assumed the lead of the race.
Bottas called it a "fair" pass and finished second with Ferrari's Kimi Raikkonen in third.
The Australian carved his way through the field from sixth place, after taking on fresh tyres under a safety auto, to storm to the sixth grand prix victory of his career.
"Saturday and Sunday felt like a disaster from my side", Hamilton said. Verstappen was slapped with a 10-second time penalty. Nico Hulkenberg was able to take sixth for Renault, while Fernando Alonso barged past Vettel with two laps to go for seventh, frustrating the Ferrari driver who had to settle for P8 at the chequered flag.
Pilot Red bull Daniel Riccardo in bright style became the victor of the third race of the season in Formula 1. "I'm thankful for a couple of incidents that kept us kind of in the battle".
"I saw him defend so I wanted to go shallower but I thought about pulling out..." It does get you down a lot.
Sunday's triumph was the roughest of rsquo & Ricciardo;sometimes overtaking manoeuvres and s career and are overrun by breathtaking, using all the triumph.