Ricciardo had closed on Rosberg's fight with the race leading Ferrari of Sebastian Vettel and, with five laps remaining, came from a long way back to lunge down the inside of the German at Turn 1.
"We know we don't have speed on the straights, but I knew were quick enough to win," Ricciardo said. "I saw Seb [Vettel] not getting away so thought if I could get Nico I could get Seb.
Rosberg cut back in front of Ricciardo at the exit, but in doing so came across the front of the RB11, with the resulting contact damaging its front wing and giving the Mercedes a puncture. Ricciardo admitted the move was bold, but said he was determined to seize his opportunity.
"I came from a long way back - I thought it was clean but Nico came back, he touched my tyre and he touched my wing. We both ruined our chance of a win, but I wanted to leave it all out there."
The collision was ultimately deemed a racing incident, and didn't prevent Ricciardo from claiming his first podium of the year - a result he dedicated to former fellow racer Jules Bianchi, who passed away last week.
"It was a crazy race," Ricciardo added. "There was contact in Turn 1, and I thought my race was over; contact on the restart with Lewis [Hamilton], and I thought my race was over; and contact with Nico as well.
"We were resilient today. I put my heart into everything today - that is way Jules would have wanted it. I feel I gained some strength today and I owe this one to him."
It was an excellent result all round for Red Bull, with Ricciardo’s team mate Daniil Kvyat taking his maiden F1 podium with second place, giving the team a welcome 33-point haul from Budapest.